$course$/top/CSSBE $course$/top/CSSBE/Sec 4 $course$/top/CSSBE/Sec 4/Fonctions $course$/top/CSSBE/Sec 4/Fonctions/2.3 - Fonction du second degré (quadratique) Caractéristiques d'une fonction quadratique Compléter à partir de la fonction quadratique ci-dessous:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»l«/mi»«mfenced»«mi»x«/mi»«/mfenced»«mo»=«/mo»«/math»#f

Ouverture de la parabole: {#1}

Abscisse du sommet: h={#2}

Ordonnée du sommet: k={#3}

Axe de symétrie: x={#4}

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xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><mi>a</mi><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mi>b</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>c</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>a</mi><mo><</mo><mn>0</mn></mrow><mrow><mi>ouverture1</mi><mo>=</mo><mo>"</mo><mi>vers</mi><mo> </mo><mi>le</mi><mo> </mo><mi>bas</mi><mo>"</mo><mo>;</mo><mo> </mo><mi>ouverture2</mi><mo>=</mo><mo>"</mo><mi>vers</mi><mo> </mo><mi>le</mi><mo> </mo><mi>haut</mi><mo>"</mo></mrow><mrow><mi>ouverture1</mi><mo>=</mo><mo>"</mo><mi>vers</mi><mo> </mo><mi>le</mi><mo> </mo><mi>haut</mi><mo>"</mo><mo>;</mo><mo> </mo><mi>ouverture2</mi><mo>=</mo><mo>"</mo><mi>vers</mi><mo> </mo><mi>le</mi><mo> </mo><mi>bas</mi><mo>"</mo></mrow></apply></math></input></command><command><input><math 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xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mfrac><mn>3</mn><mn>8</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ordonnée</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>73</mn><mn>16</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>axe</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mfrac><mn>3</mn><mn>8</mn></mfrac></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><assertions><assertion name="syntax_expression"><param name="itemseparators">;, \n</param><param name="decimalseparators">., \,</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">0.001</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option><option name="decimal_separator">,</option></options><localData><data name="inputField">textField</data><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data></localData></question> Fonction quadratique équation

Détermine l'équation de la parabole sur le graphique suivant :

#plotter1

Réponse: y = {#1}

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xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>pp</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi><mfenced><mrow><mn>2</mn><mo>,</mo><mo>-</mo><mn>2</mn></mrow></mfenced><mo> </mo><mi>in</mi><mo> </mo><mfenced><mrow><mn>4</mn><mo>,</mo><mn>5</mn></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ppp</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", $, ¥, €, £, kr, Fr, ₩, ₹, руб, BTC, %, ‰, A, K, mol, cd, rad, sr, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="decimalseparators">., \,</param><param name="unitprefixes">M, k, c, m</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">0.001</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option><option name="decimal_separator">,</option></options><localData><data name="inputField">popupEditor</data><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data></localData></question> Fonction quadratique propriétés Dans un concours de lancement de fusées miniatures, l'équipe de Raphaël a fait l'observation ci-dessous:

#plotter1

1. Que représente le domaine de cette fonction ? {#1}

2. Que représente l'image de cette fonction ? {#2}

3. Quelle est le maximum de cette fonction ? {#3} mètre(s)
]]> 3.0000000 0.3333333 0 <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>WH</mi><mo>=</mo><mn>400</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>WW</mi><mo>=</mo><mn>400</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w1</mi><mo>:</mo><mo>=</mo><mi>show_axis</mi><mo>=</mo><mi>true</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w2</mi><mo>:</mo><mo>=</mo><mi>show_grid</mi><mo>=</mo><mi>true</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w3</mi><mo>:</mo><mo>=</mo><mi>window_height</mi><mo>=</mo><mi>WH</mi></math></input></command><command><input><math 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open="{"><mtable align="center"><mtr><mtd><mo>"</mo><mi>Le</mi><mo> </mo><mi>fonctionnement</mi><mo> </mo><mi>du</mi><mo> </mo><mi>moteur</mi><mo> </mo><mi>en</mi><mo> </mo><mi>secondes</mi><mo>"</mo><mo>,</mo><mo>"</mo><mi>L</mi><mo>'</mo><mi>altitude</mi><mo> </mo><mi>en</mi><mo> </mo><mi>mètres</mi><mo>"</mo></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo>=</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>w1</mi><mo>,</mo><mi>w2</mi><mo>,</mo><mi>w3</mi><mo>,</mo><mi>w4</mi><mo>,</mo><mi>w5</mi><mo>,</mo><mi>w6</mi><mo>,</mo><mi>w7</mi><mo>,</mo><mi>w8</mi><mo>,</mo><mi>w9</mi></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>0</mn><mo>.</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>.</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math 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xmlns="http://www.w3.org/1998/Math/MathML"><mtable><mtr><mtd><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><mo>-</mo><mi>a</mi><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>h</mi><msup><mo>)</mo><mn>2</mn></msup><mo>+</mo><mi>k</mi></mtd></mtr><mtr><mtd><mi>plot</mi><mfenced><mrow><mi>f</mi><mo>,</mo><mn>0</mn><mo>.</mo><mo>.</mo><mi>h</mi></mrow></mfenced></mtd></mtr></mtable></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>plot</mi><mo>(</mo><mi>s</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>plot</mi><mo>(</mo><mi>point</mi><mo>(</mo><mi>h</mi><mo>,</mo><mi>k</mi><mo>)</mo><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>point_width</mi><mo>=</mo><mn>2</mn><mo>,</mo><mi>color</mi><mo>=</mo><mi>red</mi></mtd></mtr></mtable></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>k</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad1</mi><mo>=</mo><mi>h</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><assertions><assertion name="syntax_string"/><assertion name="equivalent_literal"><param name="usecase">false</param><param name="usespaces">false</param></assertion></assertions><options><option name="tolerance">0.001</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option><option name="float_format">,mg</option><option name="decimal_separator">,</option></options><localData><data name="inputField">textField</data><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data></localData></question> Représentation graphique d'une équation quadratique

Détermine le graphique correspondant à la fonction suivante:

#f1

]]> 1.0000000 0.3333333 0 true true none Votre réponse est correcte. Votre réponse est partiellement correcte. Votre réponse est incorrecte.

#t1

]]>

#t2

]]>

#t3

]]>

#t4

]]> <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>WH</mi><mo>=</mo><mn>400</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>WW</mi><mo>=</mo><mn>400</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w1</mi><mo>:</mo><mo>=</mo><mi>show_axis</mi><mo>=</mo><mi>true</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w2</mi><mo>:</mo><mo>=</mo><mi>show_grid</mi><mo>=</mo><mi>true</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w3</mi><mo>:</mo><mo>=</mo><mi>window_height</mi><mo>=</mo><mi>WH</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w4</mi><mo>:</mo><mo>=</mo><mi>window_width</mi><mo>=</mo><mi>WW</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w5</mi><mo>:</mo><mo>=</mo><mi>window_aspect_ratio</mi><mo>=</mo><mi>WH</mi><mo>/</mo><mi>WW</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w6</mi><mo>:</mo><mo>=</mo><mi>axis_color</mi><mo>=</mo><mi>black</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w7</mi><mo>:</mo><mo>=</mo><mi>grid_color</mi><mo>=</mo><mi>green</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w8</mi><mo>:</mo><mo>=</mo><mi>axis_style</mi><mo>=</mo><mo>"</mo><mi>arrow_xy</mi><mo>"</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w9</mi><mo>:</mo><mo>=</mo><mi>axis_label</mi><mo>=</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>x</mi><mo>,</mo><mi>y</mi></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo>=</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>w1</mi><mo>,</mo><mi>w2</mi><mo>,</mo><mi>w3</mi><mo>,</mo><mi>w4</mi><mo>,</mo><mi>w5</mi><mo>,</mo><mi>w6</mi><mo>,</mo><mi>w7</mi><mo>,</mo><mi>w8</mi><mo>,</mo><mi>w9</mi></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>2</mn><mo>.</mo><mo>.</mo><mn>2</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mo>=</mo><mi>random</mi><mo>(</mo><mo>-</mo><mn>8</mn><mo>,</mo><mn>8</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k</mi><mo>=</mo><mi>random</mi><mo>(</mo><mo>-</mo><mn>8</mn><mo>,</mo><mn>8</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f1</mi><mo>=</mo><mi>a</mi><mo>*</mo><msup><mfenced><mrow><mi>x</mi><mo>-</mo><mi>h</mi></mrow></mfenced><mn>2</mn></msup><mo>+</mo><mi>k</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f2</mi><mo>=</mo><mi>a</mi><mo>*</mo><msup><mfenced><mrow><mi>x</mi><mo>+</mo><mi>h</mi></mrow></mfenced><mn>2</mn></msup><mo>+</mo><mi>k</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f3</mi><mo>=</mo><mi>a</mi><mo>*</mo><msup><mfenced><mrow><mi>x</mi><mo>-</mo><mi>h</mi></mrow></mfenced><mn>2</mn></msup><mo>-</mo><mi>k</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f4</mi><mo>=</mo><mi>a</mi><mo>*</mo><msup><mfenced><mrow><mi>x</mi><mo>+</mo><mi>h</mi></mrow></mfenced><mn>2</mn></msup><mo>-</mo><mi>k</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tr1</mi><mo>=</mo><mi>plotter</mi><mo>(</mo><mi>point</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>0</mn><mo>)</mo><mo>,</mo><mn>31</mn><mo>,</mo><mn>31</mn><mo>,</mo><mi>W</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tr2</mi><mo>=</mo><mi>plotter</mi><mo>(</mo><mi>point</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>0</mn><mo>)</mo><mo>,</mo><mn>31</mn><mo>,</mo><mn>31</mn><mo>,</mo><mi>W</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tr3</mi><mo>=</mo><mi>plotter</mi><mo>(</mo><mi>point</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>0</mn><mo>)</mo><mo>,</mo><mn>31</mn><mo>,</mo><mn>31</mn><mo>,</mo><mi>W</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tr4</mi><mo>=</mo><mi>plotter</mi><mo>(</mo><mi>point</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>0</mn><mo>)</mo><mo>,</mo><mn>31</mn><mo>,</mo><mn>31</mn><mo>,</mo><mi>W</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t1</mi><mo>=</mo><mi>plot</mi><mo>(</mo><mi>tr1</mi><mo>,</mo><mi>f1</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t2</mi><mo>=</mo><mi>plot</mi><mo>(</mo><mi>tr2</mi><mo>,</mo><mi>f2</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t3</mi><mo>=</mo><mi>plot</mi><mo>(</mo><mi>tr3</mi><mo>,</mo><mi>f3</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t4</mi><mo>=</mo><mi>plot</mi><mo>(</mo><mi>tr4</mi><mo>,</mo><mi>f4</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><options><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data></localData></question> Fonction_quadratique_distance_points Une fonction quadratique est représentée ci-dessous. Sur cette fonction, détermine la distance entre le point d'abscisse égale à #p1 et celui d'abscisse égale à #p2.

#plotter1

]]> Le sommet de la parabole est:«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfenced»«mrow»«mo»#«/mo»«mi»h«/mi»«mo»,«/mo»«mo»§#160;«/mo»«mo»#«/mo»«mi»k«/mi»«/mrow»«/mfenced»«/math»

L'ouverture de la parabole (le paramètre: "a") est égale à: #a

Le déplacement indiqué sur le graphique ci-dessous, permet de déterminer la valeur du paramètre "a" si celui-ci est un entier.

La valeur de "a" est égale à la variation verticale illustrée par le segment de couleur rouge: #long

#plotter2

La règle de cette fonction est «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»f«/mi»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«mo»=«/mo»«/math»#z + #k

Calculons les ordonnées des points dont on connaît les abscisses:

En remplaçant #p1 dans #z + #k on obtient: #p3 et en remplaçant #p2 dans #z + #k on obtient: #p4

On doit donc calculer la distance entre les points: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfenced»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»1«/mn»«mo»,«/mo»«mo»§#160;«/mo»«mo»#«/mo»«mi»p«/mi»«mn»3«/mn»«/mrow»«/mfenced»«mo»§#160;«/mo»«mtext»et§#160;«/mtext»«mfenced»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»2«/mn»«mo»,«/mo»«mo»§#160;«/mo»«mo»#«/mo»«mi»p«/mi»«mn»4«/mn»«/mrow»«/mfenced»«/math»

En utilisant la formule de la distance on obtient: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msqrt»«msup»«mfenced»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»2«/mn»«mo»-«/mo»«mo»#«/mo»«mi»p«/mi»«mn»1«/mn»«/mrow»«/mfenced»«mn»2«/mn»«/msup»«mo»+«/mo»«msup»«mfenced»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»4«/mn»«mo»-«/mo»«mo»#«/mo»«mi»p«/mi»«mn»3«/mn»«/mrow»«/mfenced»«mn»2«/mn»«/msup»«/msqrt»«mo»=«/mo»«mo»#«/mo»«mi»s«/mi»«mi»o«/mi»«mi»l«/mi»«/math»

#plotter1

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mtext»O§#249;«/mtext»«mo»§#160;«/mo»«mi»x«/mi»«mo»:«/mo»«mtext»§#160;le§#160;temps§#160;(en§#160;sec)«/mtext»«/math»

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»f«/mi»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«mo»:«/mo»«mo»§#160;«/mo»«mtext»La§#160;hauteur§#160;du§#160;projectile§#160;(en§#160;m)«/mtext»«/math»

#plotter1

Pendant sa trajectoire, le projectile émettra une lumière lorsqu’il atteindra une hauteur de #h1 m (le point A illustre le moment où la lumière s’allumera) puis cette lumière restera allumée pendant #t1 secondes. À quelle hauteur, au centième de mètre près, sera le projectile lorsque la lumière s’éteindra (le point B illustre le moment où la lumière s’éteindra)?

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>WH</mi><mo>=</mo><mn>400</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>WW</mi><mo>=</mo><mn>400</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w1</mi><mo>:</mo><mo>=</mo><mi>show_axis</mi><mo>=</mo><mi>true</mi></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Enlever</mi><mo> </mo><mi>le</mi><mo> </mo><mi>fond</mi><mo> </mo><mi>du</mi><mo> </mo><mi>graphique</mi><mo>:</mo><mo> </mo><mi>false</mi></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w2</mi><mo>:</mo><mo>=</mo><mi>show_grid</mi><mo>=</mo><mi>false</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w3</mi><mo>:</mo><mo>=</mo><mi>window_height</mi><mo>=</mo><mi>WH</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w4</mi><mo>:</mo><mo>=</mo><mi>window_width</mi><mo>=</mo><mi>WW</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w5</mi><mo>:</mo><mo>=</mo><mi>window_aspect_ratio</mi><mo>=</mo><mi>WH</mi><mo>/</mo><mi>WW</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w6</mi><mo>:</mo><mo>=</mo><mi>axis_color</mi><mo>=</mo><mi>black</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w7</mi><mo>:</mo><mo>=</mo><mi>grid_color</mi><mo>=</mo><mi>green</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w8</mi><mo>:</mo><mo>=</mo><mi>axis_style</mi><mo>=</mo><mo>"</mo><mi>arrow_xy</mi><mo>"</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w9</mi><mo>:</mo><mo>=</mo><mi>axis_label</mi><mo>=</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>"</mo><mi>Le</mi><mo> </mo><mi>temps</mi><mo>(</mo><mi>en</mi><mo> </mo><mi>sec</mi><mo>)</mo><mo> </mo><mo>"</mo><mo>,</mo><mo>"</mo><mi>Hauteur</mi><mo> </mo><mo>(</mo><mi>en</mi><mo> </mo><mi>m</mi><mo>)</mo><mo> </mo><mo>"</mo></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo>=</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>w1</mi><mo>,</mo><mi>w2</mi><mo>,</mo><mi>w3</mi><mo>,</mo><mi>w4</mi><mo>,</mo><mi>w5</mi><mo>,</mo><mi>w6</mi><mo>,</mo><mi>w7</mi><mo>,</mo><mi>w8</mi><mo>,</mo><mi>w9</mi></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Calcul</mi><mo> </mo><mi>des</mi><mo> </mo><mi>paramètres</mi><mo> </mo><mi>de</mi><mo> </mo><mi>la</mi><mo> </mo><mi>fonction</mi><mo> </mo><mi>à</mi><mo> </mo><mi>l</mi><mo>'</mo><mi>étude</mi></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable><mtr><mtd><mi>a</mi><mo>=</mo><mo>-</mo><mn>1</mn><mo>/</mo><mi>random</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>8</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>b</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>8</mn><mo>)</mo></mtd></mtr></mtable></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Définition</mi><mo> </mo><mi>de</mi><mo> </mo><mi>la</mi><mo> </mo><mi>fonction</mi></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><mi>a</mi><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mi>b</mi><mo>*</mo><mi>x</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f1</mi><mo>=</mo><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Calcule</mi><mo> </mo><mi>de</mi><mo> </mo><mi>la</mi><mo> </mo><mi>hauteur</mi><mo> </mo><mi>maximale</mi><mo> </mo><mi>et</mi><mo> </mo><mi>du</mi><mo> </mo><mi>zéro</mi><mo> </mo><mi>le</mi><mo> </mo><mi>plus</mi><mo> </mo><mi>grand</mi></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mfenced close="⌉" open="⌈"><mfrac><mrow><mo>-</mo><msup><mi>b</mi><mn>2</mn></msup></mrow><mrow><mn>4</mn><mo>.</mo><mi>a</mi></mrow></mfrac></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mo>-</mo><mi>b</mi><mo>/</mo><mi>a</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Fenêtre</mi><mo> </mo><mi>d</mi><mo>'</mo><mi>affichage</mi></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>xval</mi><mo>=</mo><mo>-</mo><mn>2</mn><mo>*</mo><mi>b</mi><mo>/</mo><mi>a</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>yval</mi><mo>=</mo><mn>2</mn><mo>*</mo><mi>c</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tr</mi><mo>=</mo><mi>plotter</mi><mo>(</mo><mi>point</mi><mo>(</mo><mi>xval</mi><mo>/</mo><mn>4</mn><mo>,</mo><mi>yval</mi><mo>/</mo><mn>2</mn><mo>.</mo><mn>5</mn><mo>)</mo><mo>,</mo><mi>xval</mi><mo>,</mo><mi>yval</mi><mo>,</mo><mi>W</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Calcul</mi><mo> </mo><mi>d</mi><mo>'</mo><mi>une</mi><mo> </mo><mi>hauteur</mi><mo> </mo><mi>entière</mi><mo> </mo><mi>pour</mi><mo> </mo><mi>le</mi><mo> </mo><mi>point</mi><mo> </mo><mi>A</mi><mo> </mo><mi>entre</mi><mo> </mo><mn>1</mn><mo>/</mo><mn>2</mn><mo> </mo><mi>c</mi><mo> </mo><mi>et</mi><mo> </mo><mn>3</mn><mo>/</mo><mn>4</mn><mo> </mo><mi>c</mi></math></comment></maction><command><input><math 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xmlns="http://www.w3.org/1998/Math/MathML"><mi>h1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>24</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>L</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>6</mn><mo>,</mo><mn>24</mn></mtd></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>xA</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6.</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>36.</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"><param name="itemseparators">;, \n</param><param name="decimalseparators">., \,</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">0.001</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data></localData></question> $course$/top/CSSBE/Sec 4/Fonctions/2.2 - Fonction partie entière 14-Partie entière (table de valeurs)

Soit la fonction suivante:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi mathvariant=¨bold-italic¨ mathcolor=¨#00007F¨»f«/mi»«mfenced mathcolor=¨#00007F¨»«mi mathvariant=¨bold¨»x«/mi»«/mfenced»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»#«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#00007F¨»a«/mi»«mfenced open=¨[¨ close=¨]¨ mathcolor=¨#00007F¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»c«/mi»«mo mathvariant=¨bold¨»(«/mo»«mi mathvariant=¨bold¨»x«/mi»«mo mathvariant=¨bold¨»-«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»h«/mi»«mo mathvariant=¨bold¨»)«/mo»«/mrow»«/mfenced»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»+«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»#«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#00007F¨»k«/mi»«/math»

Complète la table de valeurs de cette fonction sur le domaine: #crochet1«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»e«/mi»«mo»,«/mo»«mo»#«/mo»«mi»f«/mi»«/math»#crochet2 .

Notes :

Ne laisse aucun espace entre les éléments d'une réponse.
Utilise les symboles "[" et "]" du clavier en maintenant la touche AltCar enfoncée.

x	y
{#1}	{#2}
{#3}	{#4}
{#5}	{#6}
{#7}	{#8}

]]>

x	y
{1:SA:=\#sol1}	{1:SA:=\#sol5}
{1:SA:=\#sol2}	{1:SA:=\#sol6}
{1:SA:=\#sol3}	{1:SA:=\#sol7}
{1:SA:=\#sol4}	{1:SA:=\#sol8}

]]> 8.0000000 0.3333333 0 <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Variables</mi></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>random</mi><mo>(</mo><mo>(</mo><mo>-</mo><mn>5</mn><mo>.</mo><mo>.</mo><mn>5</mn><mo>)</mo><mo>/</mo><mo>{</mo><mn>0</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mfrac><mn>1</mn><mi>b</mi></mfrac></math></input></command><command><input><math 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definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>c</mi><mo><</mo><mn>0</mn></mrow><mtable><mtr><mtd><mi>e</mi><mo>=</mo><mi>h</mi><mo>+</mo><mfrac><mn>2</mn><mi>c</mi></mfrac></mtd></mtr><mtr><mtd><mi>f</mi><mo>=</mo><mi>h</mi><mo>-</mo><mfrac><mn>2</mn><mi>c</mi></mfrac></mtd></mtr><mtr><mtd><mi>crochet1</mi><mo>=</mo><mo>"</mo><mo>]</mo><mo>"</mo></mtd></mtr><mtr><mtd><mi>crochet2</mi><mo>=</mo><mo>"</mo><mo>]</mo><mo>"</mo></mtd></mtr><mtr><mtd><mi>sol1</mi><mo>=</mo><mi>interval_open_close</mi><mo>(</mo><mi>h</mi><mo>+</mo><mfrac><mn>2</mn><mi>c</mi></mfrac><mo>,</mo><mi>h</mi><mo>+</mo><mfrac><mn>1</mn><mi>c</mi></mfrac><mo>)</mo></mtd></mtr><mtr><mtd><mi>sol2</mi><mo>=</mo><mi>interval_open_close</mi><mo>(</mo><mi>h</mi><mo>+</mo><mfrac><mn>1</mn><mi>c</mi></mfrac><mo>,</mo><mi>h</mi><mo>)</mo></mtd></mtr><mtr><mtd><mi>sol3</mi><mo>=</mo><mi>interval_open_close</mi><mo>(</mo><mi>h</mi><mo>,</mo><mi>h</mi><mo>-</mo><mfrac><mn>1</mn><mi>c</mi></mfrac><mo>)</mo></mtd></mtr><mtr><mtd><mi>sol4</mi><mo>=</mo><mi>interval_open_close</mi><mo>(</mo><mi>h</mi><mo>-</mo><mfrac><mn>1</mn><mi>c</mi></mfrac><mo>,</mo><mi>h</mi><mo>-</mo><mfrac><mn>2</mn><mi>c</mi></mfrac><mo>)</mo></mtd></mtr><mtr><mtd><mi>sol5</mi><mo>=</mo><mi>k</mi><mo>+</mo><mi>a</mi></mtd></mtr><mtr><mtd><mi>sol6</mi><mo>=</mo><mi>k</mi></mtd></mtr><mtr><mtd><mi>sol7</mi><mo>=</mo><mi>k</mi><mo>-</mo><mi>a</mi></mtd></mtr><mtr><mtd><mi>sol8</mi><mo>=</mo><mi>k</mi><mo>-</mo><mn>2</mn><mi>a</mi></mtd></mtr></mtable></apply></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Solutions</mi><mo> </mo><mi>pour</mi><mo> </mo><mi>un</mi><mo> </mo><mi>paramètre</mi><mo> </mo><mi>b</mi><mo> </mo><mi>positif</mi></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>c</mi><mo>></mo><mn>0</mn></mrow><mtable><mtr><mtd><mi>e</mi><mo>=</mo><mi>h</mi><mo>-</mo><mfrac><mn>2</mn><mi>c</mi></mfrac></mtd></mtr><mtr><mtd><mi>f</mi><mo>=</mo><mi>h</mi><mo>+</mo><mfrac><mn>2</mn><mi>c</mi></mfrac></mtd></mtr><mtr><mtd><mi>crochet1</mi><mo>=</mo><mo>"</mo><mo>[</mo><mo>"</mo></mtd></mtr><mtr><mtd><mi>crochet2</mi><mo>=</mo><mo>"</mo><mo>[</mo><mo>"</mo></mtd></mtr><mtr><mtd><mi>sol1</mi><mo>=</mo><mi>interval_close_open</mi><mo>(</mo><mi>h</mi><mo>-</mo><mfrac><mn>2</mn><mi>c</mi></mfrac><mo>,</mo><mi>h</mi><mo>-</mo><mfrac><mn>1</mn><mi>c</mi></mfrac><mo>)</mo></mtd></mtr><mtr><mtd><mi>sol2</mi><mo>=</mo><mi>interval_close_open</mi><mo>(</mo><mi>h</mi><mo>-</mo><mfrac><mn>1</mn><mi>c</mi></mfrac><mo>,</mo><mi>h</mi><mo>)</mo></mtd></mtr><mtr><mtd><mi>sol3</mi><mo>=</mo><mi>interval_close_open</mi><mo>(</mo><mi>h</mi><mo>,</mo><mi>h</mi><mo>+</mo><mfrac><mn>1</mn><mi>c</mi></mfrac><mo>)</mo></mtd></mtr><mtr><mtd><mi>sol4</mi><mo>=</mo><mi>interval_close_open</mi><mo>(</mo><mi>h</mi><mo>+</mo><mfrac><mn>1</mn><mi>c</mi></mfrac><mo>,</mo><mi>h</mi><mo>+</mo><mfrac><mn>2</mn><mi>c</mi></mfrac><mo>)</mo></mtd></mtr><mtr><mtd><mi>sol5</mi><mo>=</mo><mi>k</mi><mo>-</mo><mn>2</mn><mi>a</mi></mtd></mtr><mtr><mtd><mi>sol6</mi><mo>=</mo><mi>k</mi><mo>-</mo><mi>a</mi></mtd></mtr><mtr><mtd><mi>sol7</mi><mo>=</mo><mi>k</mi></mtd></mtr><mtr><mtd><mi>sol8</mi><mo>=</mo><mi>k</mi><mo>+</mo><mi>a</mi></mtd></mtr></mtable></apply></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>crochet1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><ms>]</ms></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>crochet2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><ms>]</ms></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mfrac><mn>1</mn><mn>3</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>11</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="]"><mrow><mo>-</mo><mn>1</mn><mo>,</mo><mn>2</mn></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="]"><mrow><mn>2</mn><mo>,</mo><mn>5</mn></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="]"><mrow><mn>5</mn><mo>,</mo><mn>8</mn></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol4</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="]"><mrow><mn>8</mn><mo>,</mo><mn>11</mn></mrow></mfenced></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><assertions><assertion name="check_simplified"/><assertion name="syntax_expression"><param name="intervals">true</param></assertion><assertion name="equivalent_equations"/></assertions><options><option name="tolerance">0.001</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data></localData></question> 15-Le forfait cellulaire.

Annabelle a échangé son vieux cellulaire contre un nouveau modèle plus performant. Le forfait qu'elle a choisi pour son nouveau cellulaire lui coûte #k $ par mois et comprend «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mfrac»«mn»1«/mn»«mn»2«/mn»«/mfrac»«mi»G«/mi»«mi»o«/mi»«/mstyle»«/math» de données mobiles.

Cependant, si elle excède sa limite de données mobiles, elle devra aussitôt payer les frais supplémentaires de #f $ qui s'ajoutent pour chaque tranche de un «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mfrac»«mn»1«/mn»«mn»2«/mn»«/mfrac»«mi»G«/mi»«mi»o«/mi»«/mstyle»«/math» .

Donne la règle qui représente cette situation.

f(x)={#1}

Combien devra-t-elle payer à la fin du mois si elle utilise 2,3 Go supplémentaires?

{#2} $

Le premier mois avec son nouveau cellulaire, Annabelle n'a pas porté attention à sa consommation de données et elle reçu une facture de 150 $. Combien de Go supplémentaires a-t-elle pu utiliser au maximum ?

Un maximum de {#3} Go a été utilisé.

]]> 3.0000000 0.3333333 0 <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Variables</mi></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>30</mn><mo>,</mo><mn>80</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mn>2</mn><mo>.</mo><mn>3</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>divisors</mi><mo>(</mo><mn>150</mn><mo>-</mo><mi>k</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>=</mo><mi>random</mi><mo>(</mo><mi>d</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>entier</mi><mo>=</mo><mfrac><mrow><mn>150</mn><mo>-</mo><mi>k</mi></mrow><mi>f</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>vmax</mi><mo>=</mo><mfrac><mrow><mi>entier</mi><mo>+</mo><mn>1</mn></mrow><mn>2</mn></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Solutions</mi></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi><mo>=</mo><mi>f</mi><mo>*</mo><mo>[</mo><mn>2</mn><mo>(</mo><mi>x</mi><mo>-</mo><mn>0</mn><mo>)</mo><mo>]</mo><mo>+</mo><mi>k</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</mi><mo>=</mo><mi>f</mi><mo>*</mo><mfenced close="⌋" open="⌊"><mrow><mn>2</mn><mi>c</mi></mrow></mfenced><mo>+</mo><mi>k</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol3</mi><mo>=</mo><mi>vmax</mi><mo>-</mo><mn>0</mn><mo>.</mo><mn>1</mn></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>39</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2.3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>1</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>37</mn><mo>,</mo><mn>111</mn></mtd></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>111</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="]" open="["><mrow><mn>222</mn><mo>*</mo><mi>x</mi></mrow></mfenced><mo>+</mo><mn>39</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>483</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0.9</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><assertions><assertion name="syntax_expression"><param name="intervals">true</param><param name="itemseparators">;, \n</param><param name="decimalseparators">., \,</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">0.001</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data></localData></question> 11 -Partie entière (réels) En évaluant la partie entière des nombres suivants, laquelle des expressions ci-dessous ne peut pas avoir un résultat égal aux autres expressions ?

]]> 4.0000000 0.3333333 0 true true none Votre réponse est correcte.

]]> Votre réponse est partiellement correcte.

]]> Votre réponse est incorrecte.

]]>

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfenced open=¨[¨ close=¨]¨»«mrow»«mo»#«/mo»«mi»c«/mi»«/mrow»«/mfenced»«/math»

]]> Cette valeur est égale à «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfenced open=¨[¨ close=¨]¨»«mrow»«mo»#«/mo»«mi»a«/mi»«/mrow»«/mfenced»«/math» et à «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfenced open=¨[¨ close=¨]¨»«msqrt»«mo»#«/mo»«mi»e«/mi»«/msqrt»«/mfenced»«/math» en prenant la racine du même signe.

]]>

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfenced open=¨[¨ close=¨]¨»«mrow»«mo»#«/mo»«mi»a«/mi»«/mrow»«/mfenced»«/math»

]]> Cette valeur est égale à «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfenced open=¨[¨ close=¨]¨»«mrow»«mo»#«/mo»«mi»c«/mi»«/mrow»«/mfenced»«/math» et «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfenced open=¨[¨ close=¨]¨»«msqrt»«mo»#«/mo»«mi»e«/mi»«/msqrt»«/mfenced»«/math» en prenant la racine du même signe.

]]>

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfenced open=¨[¨ close=¨]¨»«mrow»«mo»#«/mo»«mi»d«/mi»«/mrow»«/mfenced»«/math»

]]> Bonne réponse!

]]>

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfenced open=¨[¨ close=¨]¨»«msqrt»«mo»#«/mo»«mi»e«/mi»«/msqrt»«/mfenced»«/math»

]]> En prenant la racine du même signe la valeur est égale à «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfenced open=¨[¨ close=¨]¨»«mrow»«mo»#«/mo»«mi»c«/mi»«/mrow»«/mfenced»«/math» et à «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfenced open=¨[¨ close=¨]¨»«mrow»«mo»#«/mo»«mi»a«/mi»«/mrow»«/mfenced»«/math»

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»f«/mi»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«mo»=«/mo»«mo»#«/mo»«mi»a«/mi»«mfenced open=¨[¨ close=¨]¨»«mrow»«mo»#«/mo»«mi»b«/mi»«mo»(«/mo»«mi»x«/mi»«mo»-«/mo»«mo»#«/mo»«mi»h«/mi»«mo»)«/mo»«/mrow»«/mfenced»«mo»+«/mo»«mo»#«/mo»«mi»k«/mi»«/math»

]]> 4.0000000 0.3333333 0 true true ABCD Votre réponse est correcte.

]]> Votre réponse est partiellement correcte.

]]> Votre réponse est incorrecte.

]]>

#sol

]]> Excellent! votre réponse est juste.

]]>

#bad1

]]> Vous n'avez pas utilisé la bonne distance entre les extrémités. Il fallait utiliser la valeur de «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mn»1«/mn»«mrow»«mo»#«/mo»«mi»b«/mi»«/mrow»«/mfrac»«/math».

]]>

#bad2

]]> Il vous faut porter une attention particulière à cette notion. Pour la distance entre les extrémités, il faut utiliser la valeur «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mn»1«/mn»«mrow»«mo»#«/mo»«mi»b«/mi»«/mrow»«/mfrac»«/math». Aussi, dans votre réponse vous avez inversé la représentation des extrémités. Le paramètre b est positif donc l'extrémité fermée est située à gauche.

]]>

#bad3

]]> Vous vous êtes trompé dans la représentation des extrémités. Le paramètre b est positif donc, l'extrémité fermée est située à gauche.

]]> <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Paramètres</mi><mo> </mo><mi>de</mi><mo> </mo><mi>la</mi><mo> </mo><mi>fonction</mi><mo> </mo><mi>partie</mi><mo> </mo><mi>entère</mi><mo> </mo><mi>à</mi><mo> </mo><mi>l</mi><mo>'</mo><mi>étude</mi></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>(</mo><mn>1</mn><mo>/</mo><mn>5</mn><mo>,</mo><mn>1</mn><mo>/</mo><mn>4</mn><mo>,</mo><mn>1</mn><mo>/</mo><mn>3</mn><mo>,</mo><mn>1</mn><mo>/</mo><mn>2</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>)</mo></mtd></mtr></mtable></mfenced><mo>/</mo><mo>{</mo><mi>a</mi><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>3</mn><mo>)</mo></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Paramétrage</mi><mo> </mo><mi>de</mi><mo> </mo><mi>la</mi><mo> </mo><mi>fenêtre</mi><mo> </mo><mi>d</mi><mo>'</mo><mi>affichage</mi></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>WH</mi><mo>=</mo><mn>300</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>WW</mi><mo>=</mo><mn>300</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w1</mi><mo>:</mo><mo>=</mo><mi>show_axis</mi><mo>=</mo><mi>true</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w2</mi><mo>:</mo><mo>=</mo><mi>show_grid</mi><mo>=</mo><mi>true</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w3</mi><mo>:</mo><mo>=</mo><mi>window_height</mi><mo>=</mo><mi>WH</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w4</mi><mo>:</mo><mo>=</mo><mi>window_width</mi><mo>=</mo><mi>WW</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w5</mi><mo>:</mo><mo>=</mo><mi>window_aspect_ratio</mi><mo>=</mo><mi>WH</mi><mo>/</mo><mi>WW</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w6</mi><mo>:</mo><mo>=</mo><mi>axis_color</mi><mo>=</mo><mi>black</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w7</mi><mo>:</mo><mo>=</mo><mi>grid_color</mi><mo>=</mo><mi>green</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w8</mi><mo>:</mo><mo>=</mo><mi>axis_style</mi><mo>=</mo><mo>"</mo><mi>arrow_xy</mi><mo>"</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w9</mi><mo>:</mo><mo>=</mo><mi>axis_label</mi><mo>=</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>"</mo><mi>x</mi><mo>"</mo><mo>,</mo><mo>"</mo><mi>y</mi><mo> </mo><mo>"</mo></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo>=</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>w1</mi><mo>,</mo><mi>w2</mi><mo>,</mo><mi>w3</mi><mo>,</mo><mi>w4</mi><mo>,</mo><mi>w5</mi><mo>,</mo><mi>w6</mi><mo>,</mo><mi>w7</mi><mo>,</mo><mi>w8</mi><mo>,</mo><mi>w9</mi><mo>,</mo><mi>grid_step_x</mi><mo>=</mo><mn>1</mn><mo>/</mo><mi>b</mi><mo>,</mo><mo> </mo><mi>grid_step_y</mi><mo>=</mo><mi>a</mi></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>L</mi><mo>=</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd/></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Lg</mi><mo>=</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd/></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Ld</mi><mo>=</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd/></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Ldb</mi><mo>=</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd/></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">for</csymbol><mrow><mi>i</mi><mo> </mo><mi>in</mi><mo> </mo><mo>-</mo><mn>10</mn><mo>.</mo><mo>.</mo><mn>10</mn></mrow><mtable><mtr><mtd><mi>L</mi><mo>=</mo><mi>append</mi><mo>(</mo><mi>L</mi><mo>,</mo><mi>segment</mi><mo>(</mo><mi>point</mi><mo>(</mo><mi>i</mi><mo>/</mo><mi>b</mi><mo>+</mo><mi>h</mi><mo>,</mo><mi>i</mi><mo>*</mo><mi>a</mi><mo>+</mo><mi>k</mi><mo>)</mo><mo>,</mo><mi>point</mi><mo>(</mo><mfenced><mrow><mi>i</mi><mo>+</mo><mn>1</mn></mrow></mfenced><mo>/</mo><mi>b</mi><mo>+</mo><mi>h</mi><mo>,</mo><mi>i</mi><mo>*</mo><mi>a</mi><mo>+</mo><mi>k</mi><mo>)</mo><mo>)</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>Lg</mi><mo>=</mo><mi>append</mi><mo>(</mo><mi>Lg</mi><mo>,</mo><mi>point</mi><mo>(</mo><mi>i</mi><mo>/</mo><mi>b</mi><mo>+</mo><mi>h</mi><mo>,</mo><mi>i</mi><mo>*</mo><mi>a</mi><mo>+</mo><mi>k</mi><mo>)</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>Ld</mi><mo>=</mo><mi>append</mi><mo>(</mo><mi>Ld</mi><mo>,</mo><mi>point</mi><mo>(</mo><mfenced><mrow><mi>i</mi><mo>+</mo><mn>1</mn></mrow></mfenced><mo>/</mo><mi>b</mi><mo>+</mo><mi>h</mi><mo>,</mo><mi>i</mi><mo>*</mo><mi>a</mi><mo>+</mo><mi>k</mi><mo>)</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>Ldb</mi><mo>=</mo><mi>append</mi><mo>(</mo><mi>Ldb</mi><mo>,</mo><mi>point</mi><mo>(</mo><mfenced><mrow><mi>i</mi><mo>+</mo><mn>1</mn></mrow></mfenced><mo>/</mo><mi>b</mi><mo>+</mo><mi>h</mi><mo>,</mo><mi>i</mi><mo>*</mo><mi>a</mi><mo>+</mo><mi>k</mi><mo>)</mo><mo>)</mo></mtd></mtr></mtable></apply></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Préparation</mi><mo> </mo><mi>du</mi><mo> </mo><mi>graphique</mi></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tr</mi><mo>=</mo><mi>plotter</mi><mo>(</mo><mi>point</mi><mo>(</mo><mi>h</mi><mo>-</mo><mn>2</mn><mo>,</mo><mi>k</mi><mo>-</mo><mn>2</mn><mo>)</mo><mo>,</mo><mn>10</mn><mo>/</mo><mi>b</mi><mo>+</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>*</mo><mi>a</mi><mo>+</mo><mn>1</mn><mo>,</mo><mi>W</mi><mo>)</mo></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Traçage</mi><mo> </mo><mi>des</mi><mo> </mo><mi>segments</mi></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>plot</mi><mo>(</mo><mi>tr</mi><mo>,</mo><mi>L</mi><mo>)</mo></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Points</mi><mo> </mo><mi>aux</mi><mo> </mo><mi>extrémités</mi></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>plot</mi><mo>(</mo><mi>tr</mi><mo>,</mo><mi>Lg</mi><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>point_size</mi><mo>=</mo><mn>6</mn><mo>,</mo><mi>color</mi><mo>=</mo><mi>blue</mi></mtd></mtr></mtable></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>plot</mi><mo>(</mo><mi>tr</mi><mo>,</mo><mi>Ld</mi><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>point_size</mi><mo>=</mo><mn>6</mn><mo>,</mo><mi>color</mi><mo>=</mo><mi>blue</mi></mtd></mtr></mtable></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>plot</mi><mo>(</mo><mi>tr</mi><mo>,</mo><mi>Ldb</mi><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>point_size</mi><mo>=</mo><mn>4</mn><mo>,</mo><mi>color</mi><mo>=</mo><mi>white</mi></mtd></mtr></mtable></mfenced><mo>)</mo></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Solution</mi></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>plot</mi><mo>(</mo><mi>tr</mi><mo>,</mo><mi>L</mi><mo>)</mo></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Paramétrage</mi><mo> </mo><mi>de</mi><mo> </mo><mi>la</mi><mo> </mo><mi>fenêtre</mi><mo> </mo><mi>d</mi><mo>'</mo><mi>affichage</mi><mo> </mo><mn>2</mn></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>WH</mi><mo>=</mo><mn>300</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>WW</mi><mo>=</mo><mn>300</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w1</mi><mo>:</mo><mo>=</mo><mi>show_axis</mi><mo>=</mo><mi>true</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w2</mi><mo>:</mo><mo>=</mo><mi>show_grid</mi><mo>=</mo><mi>true</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w3</mi><mo>:</mo><mo>=</mo><mi>window_height</mi><mo>=</mo><mi>WH</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w4</mi><mo>:</mo><mo>=</mo><mi>window_width</mi><mo>=</mo><mi>WW</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w5</mi><mo>:</mo><mo>=</mo><mi>window_aspect_ratio</mi><mo>=</mo><mi>WH</mi><mo>/</mo><mi>WW</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w6</mi><mo>:</mo><mo>=</mo><mi>axis_color</mi><mo>=</mo><mi>black</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w7</mi><mo>:</mo><mo>=</mo><mi>grid_color</mi><mo>=</mo><mi>green</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w8</mi><mo>:</mo><mo>=</mo><mi>axis_style</mi><mo>=</mo><mo>"</mo><mi>arrow_xy</mi><mo>"</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w9</mi><mo>:</mo><mo>=</mo><mi>axis_label</mi><mo>=</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>"</mo><mi>x</mi><mo>"</mo><mo>,</mo><mo>"</mo><mi>y</mi><mo> </mo><mo>"</mo></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W2</mi><mo>=</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>w1</mi><mo>,</mo><mi>w2</mi><mo>,</mo><mi>w3</mi><mo>,</mo><mi>w4</mi><mo>,</mo><mi>w5</mi><mo>,</mo><mi>w6</mi><mo>,</mo><mi>w7</mi><mo>,</mo><mi>w8</mi><mo>,</mo><mi>w9</mi><mo>,</mo><mi>grid_step_x</mi><mo>=</mo><mi>b</mi><mo>,</mo><mo> </mo><mi>grid_step_y</mi><mo>=</mo><mi>a</mi></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>La</mi><mo>=</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd/></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Lb</mi><mo>=</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd/></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Lc</mi><mo>=</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd/></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Lcd</mi><mo>=</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd/></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">for</csymbol><mrow><mi>i</mi><mo> </mo><mi>in</mi><mo> </mo><mo>-</mo><mn>10</mn><mo>.</mo><mo>.</mo><mn>10</mn></mrow><mtable><mtr><mtd><mi>La</mi><mo>=</mo><mi>append</mi><mo>(</mo><mi>La</mi><mo>,</mo><mi>segment</mi><mo>(</mo><mi>point</mi><mo>(</mo><mi>i</mi><mo>*</mo><mi>b</mi><mo>+</mo><mi>h</mi><mo>,</mo><mi>i</mi><mo>*</mo><mi>a</mi><mo>+</mo><mi>k</mi><mo>)</mo><mo>,</mo><mi>point</mi><mo>(</mo><mfenced><mrow><mi>i</mi><mo>+</mo><mn>1</mn></mrow></mfenced><mo>*</mo><mi>b</mi><mo>+</mo><mi>h</mi><mo>,</mo><mi>i</mi><mo>*</mo><mi>a</mi><mo>+</mo><mi>k</mi><mo>)</mo><mo>)</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>Lb</mi><mo>=</mo><mi>append</mi><mo>(</mo><mi>Lb</mi><mo>,</mo><mi>point</mi><mo>(</mo><mi>i</mi><mo>*</mo><mi>b</mi><mo>+</mo><mi>h</mi><mo>,</mo><mi>i</mi><mo>*</mo><mi>a</mi><mo>+</mo><mi>k</mi><mo>)</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>Lc</mi><mo>=</mo><mi>append</mi><mo>(</mo><mi>Lc</mi><mo>,</mo><mi>point</mi><mo>(</mo><mfenced><mrow><mi>i</mi><mo>+</mo><mn>1</mn></mrow></mfenced><mo>*</mo><mi>b</mi><mo>+</mo><mi>h</mi><mo>,</mo><mi>i</mi><mo>*</mo><mi>a</mi><mo>+</mo><mi>k</mi><mo>)</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>Lcd</mi><mo>=</mo><mi>append</mi><mo>(</mo><mi>Lcd</mi><mo>,</mo><mi>point</mi><mo>(</mo><mfenced><mrow><mi>i</mi><mo>+</mo><mn>1</mn></mrow></mfenced><mo>*</mo><mi>b</mi><mo>+</mo><mi>h</mi><mo>,</mo><mi>i</mi><mo>*</mo><mi>a</mi><mo>+</mo><mi>k</mi><mo>)</mo><mo>)</mo></mtd></mtr></mtable></apply></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Préparation</mi><mo> </mo><mi>du</mi><mo> </mo><mi>graphique</mi><mo> </mo><mn>2</mn></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tr2</mi><mo>=</mo><mi>plotter</mi><mo>(</mo><mi>point</mi><mo>(</mo><mi>h</mi><mo>-</mo><mn>2</mn><mo>,</mo><mi>k</mi><mo>-</mo><mn>2</mn><mo>)</mo><mo>,</mo><mn>10</mn><mo>*</mo><mi>b</mi><mo>+</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>*</mo><mi>a</mi><mo>+</mo><mn>1</mn><mo>,</mo><mi>W2</mi><mo>)</mo></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Traçage</mi><mo> </mo><mi>des</mi><mo> </mo><mi>segments</mi><mo> </mo><mn>2</mn></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>plot</mi><mo>(</mo><mi>tr2</mi><mo>,</mo><mi>La</mi><mo>)</mo></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Points</mi><mo> </mo><mi>aux</mi><mo> </mo><mi>extrémités</mi><mo> </mo><mn>2</mn></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>plot</mi><mo>(</mo><mi>tr2</mi><mo>,</mo><mi>Lb</mi><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>point_size</mi><mo>=</mo><mn>6</mn><mo>,</mo><mi>color</mi><mo>=</mo><mi>blue</mi></mtd></mtr></mtable></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>plot</mi><mo>(</mo><mi>tr2</mi><mo>,</mo><mi>Lc</mi><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>point_size</mi><mo>=</mo><mn>6</mn><mo>,</mo><mi>color</mi><mo>=</mo><mi>blue</mi></mtd></mtr></mtable></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>plot</mi><mo>(</mo><mi>tr2</mi><mo>,</mo><mi>Lcd</mi><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>point_size</mi><mo>=</mo><mn>4</mn><mo>,</mo><mi>color</mi><mo>=</mo><mi>white</mi></mtd></mtr></mtable></mfenced><mo>)</mo></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Mauvaise</mi><mo> </mo><mi>solution</mi><mo> </mo><mn>1</mn></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad1</mi><mo>=</mo><mi>plot</mi><mo>(</mo><mi>tr2</mi><mo>,</mo><mi>La</mi><mo>)</mo></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Paramétrage</mi><mo> </mo><mi>de</mi><mo> </mo><mi>la</mi><mo> </mo><mi>fenêtre</mi><mo> </mo><mi>d</mi><mo>'</mo><mi>affichage</mi><mo> </mo><mn>3</mn></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>WH</mi><mo>=</mo><mn>300</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>WW</mi><mo>=</mo><mn>300</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w1</mi><mo>:</mo><mo>=</mo><mi>show_axis</mi><mo>=</mo><mi>true</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w2</mi><mo>:</mo><mo>=</mo><mi>show_grid</mi><mo>=</mo><mi>true</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w3</mi><mo>:</mo><mo>=</mo><mi>window_height</mi><mo>=</mo><mi>WH</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w4</mi><mo>:</mo><mo>=</mo><mi>window_width</mi><mo>=</mo><mi>WW</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w5</mi><mo>:</mo><mo>=</mo><mi>window_aspect_ratio</mi><mo>=</mo><mi>WH</mi><mo>/</mo><mi>WW</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w6</mi><mo>:</mo><mo>=</mo><mi>axis_color</mi><mo>=</mo><mi>black</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w7</mi><mo>:</mo><mo>=</mo><mi>grid_color</mi><mo>=</mo><mi>green</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w8</mi><mo>:</mo><mo>=</mo><mi>axis_style</mi><mo>=</mo><mo>"</mo><mi>arrow_xy</mi><mo>"</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w9</mi><mo>:</mo><mo>=</mo><mi>axis_label</mi><mo>=</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>"</mo><mi>x</mi><mo>"</mo><mo>,</mo><mo>"</mo><mi>y</mi><mo> </mo><mo>"</mo></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W3</mi><mo>=</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>w1</mi><mo>,</mo><mi>w2</mi><mo>,</mo><mi>w3</mi><mo>,</mo><mi>w4</mi><mo>,</mo><mi>w5</mi><mo>,</mo><mi>w6</mi><mo>,</mo><mi>w7</mi><mo>,</mo><mi>w8</mi><mo>,</mo><mi>w9</mi><mo>,</mo><mi>grid_step_x</mi><mo>=</mo><mi>b</mi><mo>,</mo><mo> </mo><mi>grid_step_y</mi><mo>=</mo><mi>a</mi></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Le</mi><mo>=</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd/></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Lf</mi><mo>=</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd/></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Lh</mi><mo>=</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd/></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Lfh</mi><mo>=</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd/></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">for</csymbol><mrow><mi>i</mi><mo> </mo><mi>in</mi><mo> </mo><mo>-</mo><mn>10</mn><mo>.</mo><mo>.</mo><mn>10</mn></mrow><mtable><mtr><mtd><mi>Le</mi><mo>=</mo><mi>append</mi><mo>(</mo><mi>Le</mi><mo>,</mo><mi>segment</mi><mo>(</mo><mi>point</mi><mo>(</mo><mi>i</mi><mo>*</mo><mi>b</mi><mo>+</mo><mi>h</mi><mo>,</mo><mi>i</mi><mo>*</mo><mi>a</mi><mo>+</mo><mi>k</mi><mo>)</mo><mo>,</mo><mi>point</mi><mo>(</mo><mfenced><mrow><mi>i</mi><mo>+</mo><mn>1</mn></mrow></mfenced><mo>*</mo><mi>b</mi><mo>+</mo><mi>h</mi><mo>,</mo><mi>i</mi><mo>*</mo><mi>a</mi><mo>+</mo><mi>k</mi><mo>)</mo><mo>)</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>Lf</mi><mo>=</mo><mi>append</mi><mo>(</mo><mi>Lf</mi><mo>,</mo><mi>point</mi><mo>(</mo><mi>i</mi><mo>*</mo><mi>b</mi><mo>+</mo><mi>h</mi><mo>,</mo><mi>i</mi><mo>*</mo><mi>a</mi><mo>+</mo><mi>k</mi><mo>)</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>Lh</mi><mo>=</mo><mi>append</mi><mo>(</mo><mi>Lh</mi><mo>,</mo><mi>point</mi><mo>(</mo><mfenced><mrow><mi>i</mi><mo>+</mo><mn>1</mn></mrow></mfenced><mo>*</mo><mi>b</mi><mo>+</mo><mi>h</mi><mo>,</mo><mi>i</mi><mo>*</mo><mi>a</mi><mo>+</mo><mi>k</mi><mo>)</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>Lfh</mi><mo>=</mo><mi>append</mi><mo>(</mo><mi>Lfh</mi><mo>,</mo><mi>point</mi><mo>(</mo><mi>i</mi><mo>*</mo><mi>b</mi><mo>+</mo><mi>h</mi><mo>,</mo><mi>i</mi><mo>*</mo><mi>a</mi><mo>+</mo><mi>k</mi><mo>)</mo><mo>)</mo></mtd></mtr></mtable></apply></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Préparation</mi><mo> </mo><mi>du</mi><mo> </mo><mi>graphique</mi><mo> </mo><mn>3</mn></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tr3</mi><mo>=</mo><mi>plotter</mi><mo>(</mo><mi>point</mi><mo>(</mo><mi>h</mi><mo>-</mo><mn>2</mn><mo>,</mo><mi>k</mi><mo>-</mo><mn>2</mn><mo>)</mo><mo>,</mo><mn>10</mn><mo>*</mo><mi>b</mi><mo>+</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>*</mo><mi>a</mi><mo>+</mo><mn>1</mn><mo>,</mo><mi>W3</mi><mo>)</mo></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Traçage</mi><mo> </mo><mi>des</mi><mo> </mo><mi>segments</mi><mo> </mo><mn>3</mn></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>plot</mi><mo>(</mo><mi>tr3</mi><mo>,</mo><mi>Le</mi><mo>)</mo></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Points</mi><mo> </mo><mi>aux</mi><mo> </mo><mi>extrémités</mi><mo> </mo><mn>3</mn></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>plot</mi><mo>(</mo><mi>tr3</mi><mo>,</mo><mi>Lf</mi><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>point_size</mi><mo>=</mo><mn>6</mn><mo>,</mo><mi>color</mi><mo>=</mo><mi>blue</mi></mtd></mtr></mtable></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>plot</mi><mo>(</mo><mi>tr3</mi><mo>,</mo><mi>Lh</mi><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>point_size</mi><mo>=</mo><mn>6</mn><mo>,</mo><mi>color</mi><mo>=</mo><mi>blue</mi></mtd></mtr></mtable></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>plot</mi><mo>(</mo><mi>tr3</mi><mo>,</mo><mi>Lfh</mi><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>point_size</mi><mo>=</mo><mn>4</mn><mo>,</mo><mi>color</mi><mo>=</mo><mi>white</mi></mtd></mtr></mtable></mfenced><mo>)</mo></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Mauvaise</mi><mo> </mo><mi>solution</mi><mo> </mo><mn>2</mn></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad2</mi><mo>=</mo><mi>plot</mi><mo>(</mo><mi>tr3</mi><mo>,</mo><mi>Le</mi><mo>)</mo></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Paramétrage</mi><mo> </mo><mi>de</mi><mo> </mo><mi>la</mi><mo> </mo><mi>fenêtre</mi><mo> </mo><mi>d</mi><mo>'</mo><mi>affichage</mi><mo> </mo><mn>4</mn></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>WH</mi><mo>=</mo><mn>300</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>WW</mi><mo>=</mo><mn>300</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w1</mi><mo>:</mo><mo>=</mo><mi>show_axis</mi><mo>=</mo><mi>true</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w2</mi><mo>:</mo><mo>=</mo><mi>show_grid</mi><mo>=</mo><mi>true</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w3</mi><mo>:</mo><mo>=</mo><mi>window_height</mi><mo>=</mo><mi>WH</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w4</mi><mo>:</mo><mo>=</mo><mi>window_width</mi><mo>=</mo><mi>WW</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w5</mi><mo>:</mo><mo>=</mo><mi>window_aspect_ratio</mi><mo>=</mo><mi>WH</mi><mo>/</mo><mi>WW</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w6</mi><mo>:</mo><mo>=</mo><mi>axis_color</mi><mo>=</mo><mi>black</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w7</mi><mo>:</mo><mo>=</mo><mi>grid_color</mi><mo>=</mo><mi>green</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w8</mi><mo>:</mo><mo>=</mo><mi>axis_style</mi><mo>=</mo><mo>"</mo><mi>arrow_xy</mi><mo>"</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w9</mi><mo>:</mo><mo>=</mo><mi>axis_label</mi><mo>=</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>"</mo><mi>x</mi><mo>"</mo><mo>,</mo><mo>"</mo><mi>y</mi><mo> </mo><mo>"</mo></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W4</mi><mo>=</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>w1</mi><mo>,</mo><mi>w2</mi><mo>,</mo><mi>w3</mi><mo>,</mo><mi>w4</mi><mo>,</mo><mi>w5</mi><mo>,</mo><mi>w6</mi><mo>,</mo><mi>w7</mi><mo>,</mo><mi>w8</mi><mo>,</mo><mi>w9</mi><mo>,</mo><mi>grid_step_x</mi><mo>=</mo><mn>1</mn><mo>/</mo><mi>b</mi><mo>,</mo><mo> </mo><mi>grid_step_y</mi><mo>=</mo><mi>a</mi></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Li</mi><mo>=</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd/></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Lj</mi><mo>=</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd/></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Lk</mi><mo>=</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd/></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Ljk</mi><mo>=</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd/></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">for</csymbol><mrow><mi>i</mi><mo> </mo><mi>in</mi><mo> </mo><mo>-</mo><mn>10</mn><mo>.</mo><mo>.</mo><mn>10</mn></mrow><mtable><mtr><mtd><mi>Li</mi><mo>=</mo><mi>append</mi><mo>(</mo><mi>Li</mi><mo>,</mo><mi>segment</mi><mo>(</mo><mi>point</mi><mo>(</mo><mi>i</mi><mo>/</mo><mi>b</mi><mo>+</mo><mi>h</mi><mo>,</mo><mi>i</mi><mo>*</mo><mi>a</mi><mo>+</mo><mi>k</mi><mo>)</mo><mo>,</mo><mi>point</mi><mo>(</mo><mfenced><mrow><mi>i</mi><mo>+</mo><mn>1</mn></mrow></mfenced><mo>/</mo><mi>b</mi><mo>+</mo><mi>h</mi><mo>,</mo><mi>i</mi><mo>*</mo><mi>a</mi><mo>+</mo><mi>k</mi><mo>)</mo><mo>)</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>Lj</mi><mo>=</mo><mi>append</mi><mo>(</mo><mi>Lj</mi><mo>,</mo><mi>point</mi><mo>(</mo><mi>i</mi><mo>/</mo><mi>b</mi><mo>+</mo><mi>h</mi><mo>,</mo><mi>i</mi><mo>*</mo><mi>a</mi><mo>+</mo><mi>k</mi><mo>)</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>Lk</mi><mo>=</mo><mi>append</mi><mo>(</mo><mi>Lk</mi><mo>,</mo><mi>point</mi><mo>(</mo><mfenced><mrow><mi>i</mi><mo>+</mo><mn>1</mn></mrow></mfenced><mo>/</mo><mi>b</mi><mo>+</mo><mi>h</mi><mo>,</mo><mi>i</mi><mo>*</mo><mi>a</mi><mo>+</mo><mi>k</mi><mo>)</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>Ljk</mi><mo>=</mo><mi>append</mi><mo>(</mo><mi>Ljk</mi><mo>,</mo><mi>point</mi><mo>(</mo><mi>i</mi><mo>/</mo><mi>b</mi><mo>+</mo><mi>h</mi><mo>,</mo><mi>i</mi><mo>*</mo><mi>a</mi><mo>+</mo><mi>k</mi><mo>)</mo><mo>)</mo></mtd></mtr></mtable></apply></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Préparation</mi><mo> </mo><mi>du</mi><mo> </mo><mi>graphique</mi><mo> </mo><mn>4</mn></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tr4</mi><mo>=</mo><mi>plotter</mi><mo>(</mo><mi>point</mi><mo>(</mo><mi>h</mi><mo>-</mo><mn>2</mn><mo>,</mo><mi>k</mi><mo>-</mo><mn>2</mn><mo>)</mo><mo>,</mo><mn>10</mn><mo>/</mo><mi>b</mi><mo>+</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>*</mo><mi>a</mi><mo>+</mo><mn>1</mn><mo>,</mo><mi>W</mi><mo>)</mo></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Traçage</mi><mo> </mo><mi>des</mi><mo> </mo><mi>segments</mi><mo> </mo><mn>4</mn></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>plot</mi><mo>(</mo><mi>tr4</mi><mo>,</mo><mi>Li</mi><mo>)</mo></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Points</mi><mo> </mo><mi>aux</mi><mo> </mo><mi>extrémités</mi></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>plot</mi><mo>(</mo><mi>tr4</mi><mo>,</mo><mi>Lj</mi><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>point_size</mi><mo>=</mo><mn>6</mn><mo>,</mo><mi>color</mi><mo>=</mo><mi>blue</mi></mtd></mtr></mtable></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>plot</mi><mo>(</mo><mi>tr4</mi><mo>,</mo><mi>Lk</mi><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>point_size</mi><mo>=</mo><mn>6</mn><mo>,</mo><mi>color</mi><mo>=</mo><mi>blue</mi></mtd></mtr></mtable></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>plot</mi><mo>(</mo><mi>tr4</mi><mo>,</mo><mi>Ljk</mi><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>point_size</mi><mo>=</mo><mn>4</mn><mo>,</mo><mi>color</mi><mo>=</mo><mi>white</mi></mtd></mtr></mtable></mfenced><mo>)</mo></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Mauvaise</mi><mo> </mo><mi>solution</mi><mo> </mo><mn>3</mn></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad3</mi><mo>=</mo><mi>plot</mi><mo>(</mo><mi>tr4</mi><mo>,</mo><mi>Li</mi><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><options><option name="tolerance">0.001</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option><option name="decimal_separator">,</option></options><localData><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data></localData></question> 13 -Partie entière (b négatif) Lequel des graphiques ci-dessous représente la fonction suivante:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»f«/mi»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«mo»=«/mo»«mo»#«/mo»«mi»a«/mi»«mfenced open=¨[¨ close=¨]¨»«mrow»«mo»-«/mo»«mo»#«/mo»«mi»b«/mi»«mo»(«/mo»«mi»x«/mi»«mo»-«/mo»«mo»#«/mo»«mi»h«/mi»«mo»)«/mo»«/mrow»«/mfenced»«mo»+«/mo»«mo»#«/mo»«mi»k«/mi»«/math»

]]> 4.0000000 0.3333333 0 true true ABCD Votre réponse est correcte.

]]> Votre réponse est partiellement correcte.

]]> Votre réponse est incorrecte.

]]>

#sol

]]> Excellent! votre réponse est juste.

]]>

#bad1

]]> Vous n'avez pas tenu compte de la valeur négative du paramètre b.

]]>

#bad2

]]>

#bad3

]]> Désolé, ce tracé ne correspond pas à la fonction donnée. Vous avez choisi un graphique dont les points fermés sont situés à la droite, mais vous n'avez pas tenu compte de la réflexion par rapport à l'axe vertical x=h.

]]> <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Paramètres</mi><mo> </mo><mi>de</mi><mo> </mo><mi>la</mi><mo> </mo><mi>fonction</mi><mo> </mo><mi>partie</mi><mo> </mo><mi>entère</mi><mo> </mo><mi>à</mi><mo> </mo><mi>l</mi><mo>'</mo><mi>étude</mi></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>(</mo><mn>1</mn><mo>/</mo><mn>5</mn><mo>,</mo><mn>1</mn><mo>/</mo><mn>4</mn><mo>,</mo><mn>1</mn><mo>/</mo><mn>3</mn><mo>,</mo><mn>1</mn><mo>/</mo><mn>2</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>)</mo></mtd></mtr></mtable></mfenced><mo>/</mo><mo>{</mo><mi>a</mi><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>3</mn><mo>)</mo></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Paramétrage</mi><mo> </mo><mi>de</mi><mo> </mo><mi>la</mi><mo> </mo><mi>fenêtre</mi><mo> </mo><mi>d</mi><mo>'</mo><mi>affichage1</mi></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>WH</mi><mo>=</mo><mn>300</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>WW</mi><mo>=</mo><mn>300</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w1</mi><mo>:</mo><mo>=</mo><mi>show_axis</mi><mo>=</mo><mi>true</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w2</mi><mo>:</mo><mo>=</mo><mi>show_grid</mi><mo>=</mo><mi>true</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w3</mi><mo>:</mo><mo>=</mo><mi>window_height</mi><mo>=</mo><mi>WH</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w4</mi><mo>:</mo><mo>=</mo><mi>window_width</mi><mo>=</mo><mi>WW</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w5</mi><mo>:</mo><mo>=</mo><mi>window_aspect_ratio</mi><mo>=</mo><mi>WH</mi><mo>/</mo><mi>WW</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w6</mi><mo>:</mo><mo>=</mo><mi>axis_color</mi><mo>=</mo><mi>black</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w7</mi><mo>:</mo><mo>=</mo><mi>grid_color</mi><mo>=</mo><mi>green</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w8</mi><mo>:</mo><mo>=</mo><mi>axis_style</mi><mo>=</mo><mo>"</mo><mi>arrow_xy</mi><mo>"</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w9</mi><mo>:</mo><mo>=</mo><mi>axis_label</mi><mo>=</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>"</mo><mi>x</mi><mo>"</mo><mo>,</mo><mo>"</mo><mi>y</mi><mo> </mo><mo>"</mo></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo>=</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>w1</mi><mo>,</mo><mi>w2</mi><mo>,</mo><mi>w3</mi><mo>,</mo><mi>w4</mi><mo>,</mo><mi>w5</mi><mo>,</mo><mi>w6</mi><mo>,</mo><mi>w7</mi><mo>,</mo><mi>w8</mi><mo>,</mo><mi>w9</mi><mo>,</mo><mi>grid_step_x</mi><mo>=</mo><mn>1</mn><mo>/</mo><mi>b</mi><mo>,</mo><mo> </mo><mi>grid_step_y</mi><mo>=</mo><mi>a</mi></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>L</mi><mo>=</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd/></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Lg</mi><mo>=</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd/></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Ld</mi><mo>=</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd/></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Ldb</mi><mo>=</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd/></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">for</csymbol><mrow><mi>i</mi><mo> </mo><mi>in</mi><mo> </mo><mo>-</mo><mn>10</mn><mo>.</mo><mo>.</mo><mn>10</mn></mrow><mtable><mtr><mtd><mi>L</mi><mo>=</mo><mi>append</mi><mo>(</mo><mi>L</mi><mo>,</mo><mi>segment</mi><mo>(</mo><mi>point</mi><mo>(</mo><mfenced><mrow><mi>i</mi><mo>+</mo><mn>1</mn></mrow></mfenced><mo>/</mo><mo>-</mo><mi>b</mi><mo>+</mo><mi>h</mi><mo>,</mo><mi>i</mi><mo>*</mo><mi>a</mi><mo>+</mo><mi>k</mi><mo>)</mo><mo>,</mo><mi>point</mi><mo>(</mo><mi>i</mi><mo>/</mo><mo>-</mo><mi>b</mi><mo>+</mo><mi>h</mi><mo>,</mo><mi>i</mi><mo>*</mo><mi>a</mi><mo>+</mo><mi>k</mi><mo>)</mo><mo>)</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>Lg</mi><mo>=</mo><mi>append</mi><mo>(</mo><mi>Lg</mi><mo>,</mo><mi>point</mi><mo>(</mo><mi>i</mi><mo>/</mo><mo>-</mo><mi>b</mi><mo>+</mo><mi>h</mi><mo>,</mo><mi>i</mi><mo>*</mo><mi>a</mi><mo>+</mo><mi>k</mi><mo>)</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>Ld</mi><mo>=</mo><mi>append</mi><mo>(</mo><mi>Ld</mi><mo>,</mo><mi>point</mi><mo>(</mo><mfenced><mrow><mi>i</mi><mo>+</mo><mn>1</mn></mrow></mfenced><mo>/</mo><mo>-</mo><mi>b</mi><mo>+</mo><mi>h</mi><mo>,</mo><mi>i</mi><mo>*</mo><mi>a</mi><mo>+</mo><mi>k</mi><mo>)</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>Ldb</mi><mo>=</mo><mi>append</mi><mo>(</mo><mi>Ldb</mi><mo>,</mo><mi>point</mi><mo>(</mo><mfenced><mrow><mi>i</mi><mo>+</mo><mn>1</mn></mrow></mfenced><mo>/</mo><mo>-</mo><mi>b</mi><mo>+</mo><mi>h</mi><mo>,</mo><mi>i</mi><mo>*</mo><mi>a</mi><mo>+</mo><mi>k</mi><mo>)</mo><mo>)</mo></mtd></mtr></mtable></apply></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Préparation</mi><mo> </mo><mi>du</mi><mo> </mo><mi>graphique1</mi></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tr</mi><mo>=</mo><mi>plotter</mi><mo>(</mo><mi>point</mi><mo>(</mo><mi>h</mi><mo>-</mo><mn>2</mn><mo>,</mo><mi>k</mi><mo>-</mo><mn>2</mn><mo>)</mo><mo>,</mo><mn>10</mn><mo>/</mo><mi>b</mi><mo>+</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>*</mo><mi>a</mi><mo>+</mo><mn>1</mn><mo>,</mo><mi>W</mi><mo>)</mo></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Traçage</mi><mo> </mo><mi>des</mi><mo> </mo><mi>segments1</mi></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>plot</mi><mo>(</mo><mi>tr</mi><mo>,</mo><mi>L</mi><mo>)</mo></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Points</mi><mo> </mo><mi>aux</mi><mo> </mo><mi>extrémités1</mi></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>plot</mi><mo>(</mo><mi>tr</mi><mo>,</mo><mi>Lg</mi><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>point_size</mi><mo>=</mo><mn>6</mn><mo>,</mo><mi>color</mi><mo>=</mo><mi>blue</mi></mtd></mtr></mtable></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>plot</mi><mo>(</mo><mi>tr</mi><mo>,</mo><mi>Ld</mi><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>point_size</mi><mo>=</mo><mn>6</mn><mo>,</mo><mi>color</mi><mo>=</mo><mi>blue</mi></mtd></mtr></mtable></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>plot</mi><mo>(</mo><mi>tr</mi><mo>,</mo><mi>Ldb</mi><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>point_size</mi><mo>=</mo><mn>4</mn><mo>,</mo><mi>color</mi><mo>=</mo><mi>white</mi></mtd></mtr></mtable></mfenced><mo>)</mo></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Solution</mi></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>plot</mi><mo>(</mo><mi>tr</mi><mo>,</mo><mi>L</mi><mo>)</mo></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Paramétrage</mi><mo> </mo><mi>de</mi><mo> </mo><mi>la</mi><mo> </mo><mi>fenêtre</mi><mo> </mo><mi>d</mi><mo>'</mo><mi>affichage</mi><mo> </mo><mn>2</mn></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>WH</mi><mo>=</mo><mn>300</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>WW</mi><mo>=</mo><mn>300</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w1</mi><mo>:</mo><mo>=</mo><mi>show_axis</mi><mo>=</mo><mi>true</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w2</mi><mo>:</mo><mo>=</mo><mi>show_grid</mi><mo>=</mo><mi>true</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w3</mi><mo>:</mo><mo>=</mo><mi>window_height</mi><mo>=</mo><mi>WH</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w4</mi><mo>:</mo><mo>=</mo><mi>window_width</mi><mo>=</mo><mi>WW</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w5</mi><mo>:</mo><mo>=</mo><mi>window_aspect_ratio</mi><mo>=</mo><mi>WH</mi><mo>/</mo><mi>WW</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w6</mi><mo>:</mo><mo>=</mo><mi>axis_color</mi><mo>=</mo><mi>black</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w7</mi><mo>:</mo><mo>=</mo><mi>grid_color</mi><mo>=</mo><mi>green</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w8</mi><mo>:</mo><mo>=</mo><mi>axis_style</mi><mo>=</mo><mo>"</mo><mi>arrow_xy</mi><mo>"</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w9</mi><mo>:</mo><mo>=</mo><mi>axis_label</mi><mo>=</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>"</mo><mi>x</mi><mo>"</mo><mo>,</mo><mo>"</mo><mi>y</mi><mo> </mo><mo>"</mo></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W2</mi><mo>=</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>w1</mi><mo>,</mo><mi>w2</mi><mo>,</mo><mi>w3</mi><mo>,</mo><mi>w4</mi><mo>,</mo><mi>w5</mi><mo>,</mo><mi>w6</mi><mo>,</mo><mi>w7</mi><mo>,</mo><mi>w8</mi><mo>,</mo><mi>w9</mi><mo>,</mo><mi>grid_step_x</mi><mo>=</mo><mn>1</mn><mo>/</mo><mi>b</mi><mo>,</mo><mo> </mo><mi>grid_step_y</mi><mo>=</mo><mi>a</mi></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>La</mi><mo>=</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd/></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Lb</mi><mo>=</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd/></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Lc</mi><mo>=</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd/></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Lz</mi><mo>=</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd/></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">for</csymbol><mrow><mi>i</mi><mo> </mo><mi>in</mi><mo> </mo><mo>-</mo><mn>10</mn><mo>.</mo><mo>.</mo><mn>10</mn></mrow><mtable><mtr><mtd><mi>La</mi><mo>=</mo><mi>append</mi><mo>(</mo><mi>La</mi><mo>,</mo><mi>segment</mi><mo>(</mo><mi>point</mi><mo>(</mo><mi>i</mi><mo>/</mo><mi>b</mi><mo>+</mo><mi>h</mi><mo>,</mo><mi>i</mi><mo>*</mo><mi>a</mi><mo>+</mo><mi>k</mi><mo>)</mo><mo>,</mo><mi>point</mi><mo>(</mo><mfenced><mrow><mi>i</mi><mo>+</mo><mn>1</mn></mrow></mfenced><mo>/</mo><mi>b</mi><mo>+</mo><mi>h</mi><mo>,</mo><mi>i</mi><mo>*</mo><mi>a</mi><mo>+</mo><mi>k</mi><mo>)</mo><mo>)</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>Lb</mi><mo>=</mo><mi>append</mi><mo>(</mo><mi>Lb</mi><mo>,</mo><mi>point</mi><mo>(</mo><mi>i</mi><mo>/</mo><mi>b</mi><mo>+</mo><mi>h</mi><mo>,</mo><mi>i</mi><mo>*</mo><mi>a</mi><mo>+</mo><mi>k</mi><mo>)</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>Lc</mi><mo>=</mo><mi>append</mi><mo>(</mo><mi>Lc</mi><mo>,</mo><mi>point</mi><mo>(</mo><mfenced><mrow><mi>i</mi><mo>+</mo><mn>1</mn></mrow></mfenced><mo>/</mo><mi>b</mi><mo>+</mo><mi>h</mi><mo>,</mo><mi>i</mi><mo>*</mo><mi>a</mi><mo>+</mo><mi>k</mi><mo>)</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>Lz</mi><mo>=</mo><mi>append</mi><mo>(</mo><mi>Lz</mi><mo>,</mo><mi>point</mi><mo>(</mo><mfenced><mrow><mi>i</mi><mo>+</mo><mn>1</mn></mrow></mfenced><mo>/</mo><mi>b</mi><mo>+</mo><mi>h</mi><mo>,</mo><mi>i</mi><mo>*</mo><mi>a</mi><mo>+</mo><mi>k</mi><mo>)</mo><mo>)</mo></mtd></mtr></mtable></apply></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Préparation</mi><mo> </mo><mi>du</mi><mo> </mo><mi>graphique</mi><mo> </mo><mn>2</mn></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tr2</mi><mo>=</mo><mi>plotter</mi><mo>(</mo><mi>point</mi><mo>(</mo><mi>h</mi><mo>-</mo><mn>2</mn><mo>,</mo><mi>k</mi><mo>-</mo><mn>2</mn><mo>)</mo><mo>,</mo><mn>10</mn><mo>/</mo><mi>b</mi><mo>+</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>*</mo><mi>a</mi><mo>+</mo><mn>1</mn><mo>,</mo><mi>W2</mi><mo>)</mo></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Traçage</mi><mo> </mo><mi>des</mi><mo> </mo><mi>segments</mi><mo> </mo><mn>2</mn></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>plot</mi><mo>(</mo><mi>tr2</mi><mo>,</mo><mi>La</mi><mo>)</mo></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Points</mi><mo> </mo><mi>aux</mi><mo> </mo><mi>extrémités</mi><mo> </mo><mn>2</mn></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>plot</mi><mo>(</mo><mi>tr2</mi><mo>,</mo><mi>Lb</mi><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>point_size</mi><mo>=</mo><mn>6</mn><mo>,</mo><mi>color</mi><mo>=</mo><mi>blue</mi></mtd></mtr></mtable></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>plot</mi><mo>(</mo><mi>tr2</mi><mo>,</mo><mi>Lc</mi><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>point_size</mi><mo>=</mo><mn>6</mn><mo>,</mo><mi>color</mi><mo>=</mo><mi>blue</mi></mtd></mtr></mtable></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>plot</mi><mo>(</mo><mi>tr2</mi><mo>,</mo><mi>Lz</mi><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>point_size</mi><mo>=</mo><mn>4</mn><mo>,</mo><mi>color</mi><mo>=</mo><mi>white</mi></mtd></mtr></mtable></mfenced><mo>)</mo></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Mauvaise</mi><mo> </mo><mi>solution</mi><mo> </mo><mn>1</mn></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad1</mi><mo>=</mo><mi>plot</mi><mo>(</mo><mi>tr2</mi><mo>,</mo><mi>La</mi><mo>)</mo></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Paramétrage</mi><mo> </mo><mi>de</mi><mo> </mo><mi>la</mi><mo> </mo><mi>fenêtre</mi><mo> </mo><mi>d</mi><mo>'</mo><mi>affichage</mi><mo> </mo><mn>3</mn></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>WH</mi><mo>=</mo><mn>300</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>WW</mi><mo>=</mo><mn>300</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w1</mi><mo>:</mo><mo>=</mo><mi>show_axis</mi><mo>=</mo><mi>true</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w2</mi><mo>:</mo><mo>=</mo><mi>show_grid</mi><mo>=</mo><mi>true</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w3</mi><mo>:</mo><mo>=</mo><mi>window_height</mi><mo>=</mo><mi>WH</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w4</mi><mo>:</mo><mo>=</mo><mi>window_width</mi><mo>=</mo><mi>WW</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w5</mi><mo>:</mo><mo>=</mo><mi>window_aspect_ratio</mi><mo>=</mo><mi>WH</mi><mo>/</mo><mi>WW</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w6</mi><mo>:</mo><mo>=</mo><mi>axis_color</mi><mo>=</mo><mi>black</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w7</mi><mo>:</mo><mo>=</mo><mi>grid_color</mi><mo>=</mo><mi>green</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w8</mi><mo>:</mo><mo>=</mo><mi>axis_style</mi><mo>=</mo><mo>"</mo><mi>arrow_xy</mi><mo>"</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w9</mi><mo>:</mo><mo>=</mo><mi>axis_label</mi><mo>=</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>"</mo><mi>x</mi><mo>"</mo><mo>,</mo><mo>"</mo><mi>y</mi><mo> </mo><mo>"</mo></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W3</mi><mo>=</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>w1</mi><mo>,</mo><mi>w2</mi><mo>,</mo><mi>w3</mi><mo>,</mo><mi>w4</mi><mo>,</mo><mi>w5</mi><mo>,</mo><mi>w6</mi><mo>,</mo><mi>w7</mi><mo>,</mo><mi>w8</mi><mo>,</mo><mi>w9</mi><mo>,</mo><mi>grid_step_x</mi><mo>=</mo><mi>b</mi><mo>,</mo><mo> </mo><mi>grid_step_y</mi><mo>=</mo><mi>a</mi></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Le</mi><mo>=</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd/></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Lf</mi><mo>=</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd/></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Lh</mi><mo>=</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd/></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Lfh</mi><mo>=</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd/></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">for</csymbol><mrow><mi>i</mi><mo> </mo><mi>in</mi><mo> </mo><mo>-</mo><mn>10</mn><mo>.</mo><mo>.</mo><mn>10</mn></mrow><mtable><mtr><mtd><mi>Le</mi><mo>=</mo><mi>append</mi><mo>(</mo><mi>Le</mi><mo>,</mo><mi>segment</mi><mo>(</mo><mi>point</mi><mo>(</mo><mfenced><mrow><mi>i</mi><mo>+</mo><mn>1</mn></mrow></mfenced><mo>*</mo><mo>-</mo><mi>b</mi><mo>+</mo><mi>h</mi><mo>,</mo><mi>i</mi><mo>*</mo><mi>a</mi><mo>+</mo><mi>k</mi><mo>)</mo><mo>,</mo><mi>point</mi><mo>(</mo><mi>i</mi><mo>*</mo><mo>-</mo><mi>b</mi><mo>+</mo><mi>h</mi><mo>,</mo><mi>i</mi><mo>*</mo><mi>a</mi><mo>+</mo><mi>k</mi><mo>)</mo><mo>)</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>Lf</mi><mo>=</mo><mi>append</mi><mo>(</mo><mi>Lf</mi><mo>,</mo><mi>point</mi><mo>(</mo><mi>i</mi><mo>*</mo><mo>-</mo><mi>b</mi><mo>+</mo><mi>h</mi><mo>,</mo><mi>i</mi><mo>*</mo><mi>a</mi><mo>+</mo><mi>k</mi><mo>)</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>Lh</mi><mo>=</mo><mi>append</mi><mo>(</mo><mi>Lh</mi><mo>,</mo><mi>point</mi><mo>(</mo><mfenced><mrow><mi>i</mi><mo>+</mo><mn>1</mn></mrow></mfenced><mo>*</mo><mo>-</mo><mi>b</mi><mo>+</mo><mi>h</mi><mo>,</mo><mi>i</mi><mo>*</mo><mi>a</mi><mo>+</mo><mi>k</mi><mo>)</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>Lfh</mi><mo>=</mo><mi>append</mi><mo>(</mo><mi>Lfh</mi><mo>,</mo><mi>point</mi><mo>(</mo><mi>i</mi><mo>*</mo><mo>-</mo><mi>b</mi><mo>+</mo><mi>h</mi><mo>,</mo><mi>i</mi><mo>*</mo><mi>a</mi><mo>+</mo><mi>k</mi><mo>)</mo><mo>)</mo></mtd></mtr></mtable></apply></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Préparation</mi><mo> </mo><mi>du</mi><mo> </mo><mi>graphique</mi><mo> </mo><mn>3</mn></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tr3</mi><mo>=</mo><mi>plotter</mi><mo>(</mo><mi>point</mi><mo>(</mo><mi>h</mi><mo>-</mo><mn>1</mn><mo>,</mo><mi>k</mi><mo>-</mo><mn>1</mn><mo>)</mo><mo>,</mo><mn>10</mn><mo>*</mo><mi>b</mi><mo>+</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>*</mo><mi>a</mi><mo>+</mo><mn>1</mn><mo>,</mo><mi>W3</mi><mo>)</mo></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Traçage</mi><mo> </mo><mi>des</mi><mo> </mo><mi>segments</mi><mo> </mo><mn>3</mn></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>plot</mi><mo>(</mo><mi>tr3</mi><mo>,</mo><mi>Le</mi><mo>)</mo></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Points</mi><mo> </mo><mi>aux</mi><mo> </mo><mi>extrémités</mi><mo> </mo><mn>3</mn></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>plot</mi><mo>(</mo><mi>tr3</mi><mo>,</mo><mi>Lf</mi><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>point_size</mi><mo>=</mo><mn>6</mn><mo>,</mo><mi>color</mi><mo>=</mo><mi>blue</mi></mtd></mtr></mtable></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>plot</mi><mo>(</mo><mi>tr3</mi><mo>,</mo><mi>Lh</mi><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>point_size</mi><mo>=</mo><mn>6</mn><mo>,</mo><mi>color</mi><mo>=</mo><mi>blue</mi></mtd></mtr></mtable></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>plot</mi><mo>(</mo><mi>tr3</mi><mo>,</mo><mi>Lfh</mi><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>point_size</mi><mo>=</mo><mn>4</mn><mo>,</mo><mi>color</mi><mo>=</mo><mi>white</mi></mtd></mtr></mtable></mfenced><mo>)</mo></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Mauvaise</mi><mo> </mo><mi>solution</mi><mo> </mo><mn>2</mn></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad2</mi><mo>=</mo><mi>plot</mi><mo>(</mo><mi>tr3</mi><mo>,</mo><mi>Le</mi><mo>)</mo></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Paramétrage</mi><mo> </mo><mi>de</mi><mo> </mo><mi>la</mi><mo> </mo><mi>fenêtre</mi><mo> </mo><mi>d</mi><mo>'</mo><mi>affichage</mi><mo> </mo><mn>4</mn></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>WH</mi><mo>=</mo><mn>300</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>WW</mi><mo>=</mo><mn>300</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w1</mi><mo>:</mo><mo>=</mo><mi>show_axis</mi><mo>=</mo><mi>true</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w2</mi><mo>:</mo><mo>=</mo><mi>show_grid</mi><mo>=</mo><mi>true</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w3</mi><mo>:</mo><mo>=</mo><mi>window_height</mi><mo>=</mo><mi>WH</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w4</mi><mo>:</mo><mo>=</mo><mi>window_width</mi><mo>=</mo><mi>WW</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w5</mi><mo>:</mo><mo>=</mo><mi>window_aspect_ratio</mi><mo>=</mo><mi>WH</mi><mo>/</mo><mi>WW</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w6</mi><mo>:</mo><mo>=</mo><mi>axis_color</mi><mo>=</mo><mi>black</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w7</mi><mo>:</mo><mo>=</mo><mi>grid_color</mi><mo>=</mo><mi>green</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w8</mi><mo>:</mo><mo>=</mo><mi>axis_style</mi><mo>=</mo><mo>"</mo><mi>arrow_xy</mi><mo>"</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w9</mi><mo>:</mo><mo>=</mo><mi>axis_label</mi><mo>=</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>"</mo><mi>x</mi><mo>"</mo><mo>,</mo><mo>"</mo><mi>y</mi><mo> </mo><mo>"</mo></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W4</mi><mo>=</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>w1</mi><mo>,</mo><mi>w2</mi><mo>,</mo><mi>w3</mi><mo>,</mo><mi>w4</mi><mo>,</mo><mi>w5</mi><mo>,</mo><mi>w6</mi><mo>,</mo><mi>w7</mi><mo>,</mo><mi>w8</mi><mo>,</mo><mi>w9</mi><mo>,</mo><mi>grid_step_x</mi><mo>=</mo><mn>1</mn><mo>/</mo><mi>b</mi><mo>,</mo><mo> </mo><mi>grid_step_y</mi><mo>=</mo><mi>a</mi></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Li</mi><mo>=</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd/></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Lj</mi><mo>=</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd/></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Lk</mi><mo>=</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd/></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Ljk</mi><mo>=</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd/></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">for</csymbol><mrow><mi>i</mi><mo> </mo><mi>in</mi><mo> </mo><mo>-</mo><mn>10</mn><mo>.</mo><mo>.</mo><mn>10</mn></mrow><mtable><mtr><mtd><mi>Li</mi><mo>=</mo><mi>append</mi><mo>(</mo><mi>Li</mi><mo>,</mo><mi>segment</mi><mo>(</mo><mi>point</mi><mo>(</mo><mi>i</mi><mo>/</mo><mi>b</mi><mo>+</mo><mi>h</mi><mo>,</mo><mi>i</mi><mo>*</mo><mi>a</mi><mo>+</mo><mi>k</mi><mo>)</mo><mo>,</mo><mi>point</mi><mo>(</mo><mfenced><mrow><mi>i</mi><mo>+</mo><mn>1</mn></mrow></mfenced><mo>/</mo><mi>b</mi><mo>+</mo><mi>h</mi><mo>,</mo><mi>i</mi><mo>*</mo><mi>a</mi><mo>+</mo><mi>k</mi><mo>)</mo><mo>)</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>Lj</mi><mo>=</mo><mi>append</mi><mo>(</mo><mi>Lj</mi><mo>,</mo><mi>point</mi><mo>(</mo><mi>i</mi><mo>/</mo><mi>b</mi><mo>+</mo><mi>h</mi><mo>,</mo><mi>i</mi><mo>*</mo><mi>a</mi><mo>+</mo><mi>k</mi><mo>)</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>Lk</mi><mo>=</mo><mi>append</mi><mo>(</mo><mi>Lk</mi><mo>,</mo><mi>point</mi><mo>(</mo><mfenced><mrow><mi>i</mi><mo>+</mo><mn>1</mn></mrow></mfenced><mo>/</mo><mi>b</mi><mo>+</mo><mi>h</mi><mo>,</mo><mi>i</mi><mo>*</mo><mi>a</mi><mo>+</mo><mi>k</mi><mo>)</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>Ljk</mi><mo>=</mo><mi>append</mi><mo>(</mo><mi>Ljk</mi><mo>,</mo><mi>point</mi><mo>(</mo><mi>i</mi><mo>/</mo><mi>b</mi><mo>+</mo><mi>h</mi><mo>,</mo><mi>i</mi><mo>*</mo><mi>a</mi><mo>+</mo><mi>k</mi><mo>)</mo><mo>)</mo></mtd></mtr></mtable></apply></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Préparation</mi><mo> </mo><mi>du</mi><mo> </mo><mi>graphique</mi><mo> </mo><mn>4</mn></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tr4</mi><mo>=</mo><mi>plotter</mi><mo>(</mo><mi>point</mi><mo>(</mo><mi>h</mi><mo>-</mo><mn>2</mn><mo>,</mo><mi>k</mi><mo>-</mo><mn>2</mn><mo>)</mo><mo>,</mo><mn>10</mn><mo>/</mo><mi>b</mi><mo>+</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>*</mo><mi>a</mi><mo>+</mo><mn>1</mn><mo>,</mo><mi>W</mi><mo>)</mo></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Traçage</mi><mo> </mo><mi>des</mi><mo> </mo><mi>segments</mi><mo> </mo><mn>4</mn></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>plot</mi><mo>(</mo><mi>tr4</mi><mo>,</mo><mi>Li</mi><mo>)</mo></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Points</mi><mo> </mo><mi>aux</mi><mo> </mo><mi>extrémités</mi></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>plot</mi><mo>(</mo><mi>tr4</mi><mo>,</mo><mi>Lj</mi><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>point_size</mi><mo>=</mo><mn>6</mn><mo>,</mo><mi>color</mi><mo>=</mo><mi>blue</mi></mtd></mtr></mtable></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>plot</mi><mo>(</mo><mi>tr4</mi><mo>,</mo><mi>Lk</mi><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>point_size</mi><mo>=</mo><mn>6</mn><mo>,</mo><mi>color</mi><mo>=</mo><mi>blue</mi></mtd></mtr></mtable></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>plot</mi><mo>(</mo><mi>tr4</mi><mo>,</mo><mi>Ljk</mi><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>point_size</mi><mo>=</mo><mn>4</mn><mo>,</mo><mi>color</mi><mo>=</mo><mi>white</mi></mtd></mtr></mtable></mfenced><mo>)</mo></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Mauvaise</mi><mo> </mo><mi>solution</mi><mo> </mo><mn>3</mn></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad3</mi><mo>=</mo><mi>plot</mi><mo>(</mo><mi>tr4</mi><mo>,</mo><mi>Li</mi><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>1</mn><mn>5</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><options><option name="tolerance">0.001</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator"></option><option name="implicit_times_operator">true</option><option name="imaginary_unit"></option><option name="decimal_separator">,</option></options><localData><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data></localData></question> Partie_entière_1 Quel choix représente la somme de l'expression donnée ci-dessous lorsque l'on remplace x par #x1 et y par #y1?

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfenced open=¨[¨ close=¨]¨»«mi»x«/mi»«/mfenced»«mo»+«/mo»«mfenced open=¨[¨ close=¨]¨»«mi»y«/mi»«/mfenced»«mo»=«/mo»«mo»?«/mo»«/math»

]]> 1.0000000 0.3333333 0 true true none Votre réponse est correcte.

]]> Votre réponse est partiellement correcte.

]]> Votre réponse est incorrecte.

]]> #sol

]]> #bad1

]]> #bad2

]]> #bad3

]]> <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>x1</mi><mo>=</mo><mi>random</mi><mo>(</mo><mo>-</mo><mn>100</mn><mo>.</mo><mo>.</mo><mn>100</mn><mo>.</mo><mo>.</mo><mn>0</mn><mo>.</mo><mn>01</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>y1</mi><mo>=</mo><mi>random</mi><mo>(</mo><mo>-</mo><mn>100</mn><mo>.</mo><mo>.</mo><mn>100</mn><mo>.</mo><mo>.</mo><mn>0</mn><mo>.</mo><mn>01</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>sol</mi><mo>=</mo><mfenced close="⌋" open="⌊"><mi>x1</mi></mfenced><mo>+</mo><mfenced close="⌋" open="⌊"><mi>y1</mi></mfenced></mtd></mtr><mtr><mtd><mi>bad2</mi><mo>=</mo><mfenced close="⌋" open="⌊"><mrow><mi>x1</mi><mo>+</mo><mi>y1</mi></mrow></mfenced></mtd></mtr><mtr><mtd><mi>bad1</mi><mo>=</mo><mfenced close="|" open="|"><mi>x1</mi></mfenced><mo>+</mo><mfenced close="|" open="|"><mi>y1</mi></mfenced></mtd></mtr></mtable><mrow><mi>sol</mi><mo>≠</mo><mi>bad2</mi><mo>∧</mo><mi>sol</mi><mo>≠</mo><mi>bad1</mi></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad3</mi><mo>=</mo><mfenced close="⌉" open="⌈"><mi>x1</mi></mfenced><mo>+</mo><mfenced close="⌉" open="⌈"><mi>y1</mi></mfenced></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>48.07</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>17.74</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>67</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>65.81</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>66</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>65</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><options><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option><option name="decimal_separator">,</option></options><localData><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data></localData></question> Partie_entière_2 Quel choix représente le résultat de l'expression ci-dessous lorsque l'on remplace x par #x1 et y par #y1?

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»a«/mi»«mo»§#160;«/mo»«mfenced open=¨[¨ close=¨]¨»«mi»x«/mi»«/mfenced»«mo»-«/mo»«mfenced open=¨[¨ close=¨]¨»«mi»y«/mi»«/mfenced»«mo»=«/mo»«mo»?«/mo»«/math»

]]> 1.0000000 0.3333333 0 true true none Votre réponse est correcte.

]]> Votre réponse est partiellement correcte.

]]> Votre réponse est incorrecte.

]]> #sol

]]> #bad1

]]> #bad2

]]> #bad3

]]> <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>x1</mi><mo>=</mo><mi>random</mi><mo>(</mo><mo>-</mo><mn>100</mn><mo>.</mo><mo>.</mo><mn>100</mn><mo>.</mo><mo>.</mo><mn>0</mn><mo>.</mo><mn>01</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>y1</mi><mo>=</mo><mi>random</mi><mo>(</mo><mo>-</mo><mn>100</mn><mo>.</mo><mo>.</mo><mn>100</mn><mo>.</mo><mo>.</mo><mn>0</mn><mo>.</mo><mn>01</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>a</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>10</mn><mo>.</mo><mo>.</mo><mn>10</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></mtd></mtr><mtr><mtd><mi>bad1</mi><mo>=</mo><mi>a</mi><mo>*</mo><mfenced close="|" open="|"><mi>x1</mi></mfenced><mo>-</mo><mfenced close="|" open="|"><mi>y1</mi></mfenced></mtd></mtr><mtr><mtd><mi>sol</mi><mo>=</mo><mi>a</mi><mo>*</mo><mfenced close="⌋" open="⌊"><mi>x1</mi></mfenced><mo>-</mo><mfenced close="⌋" open="⌊"><mi>y1</mi></mfenced></mtd></mtr><mtr><mtd><mi>bad2</mi><mo>=</mo><mi>a</mi><mo>*</mo><mfenced close="⌋" open="⌊"><mrow><mi>x1</mi><mo>-</mo><mi>y1</mi></mrow></mfenced></mtd></mtr></mtable><mrow><mi>sol</mi><mo>≠</mo><mi>bad2</mi><mo>∧</mo><mi>sol</mi><mo>≠</mo><mi>bad1</mi></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad3</mi><mo>=</mo><mi>a</mi><mo>*</mo><mfenced close="⌉" open="⌈"><mi>x1</mi></mfenced><mo>-</mo><mfenced close="⌉" open="⌈"><mi>y1</mi></mfenced></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>48.84</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>86.99</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>576</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>401.41</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>1360</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>567</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><options><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option><option name="decimal_separator">,</option></options><localData><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data></localData></question> Partie_entière_3 Quel choix représente le résultat de l'expression ci-dessous lorsque l'on remplace x par #x1 et y par #y1?

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»a«/mi»«mo»§#160;«/mo»«mfenced open=¨[¨ close=¨]¨»«mi»x«/mi»«/mfenced»«mo»+«/mo»«mo»#«/mo»«mi»b«/mi»«mo»§#160;«/mo»«mfenced open=¨[¨ close=¨]¨»«mi»y«/mi»«/mfenced»«mo»=«/mo»«mo»?«/mo»«/math»

]]> 1.0000000 0.3333333 0 true true none Votre réponse est correcte.

]]> Votre réponse est partiellement correcte.

]]> Votre réponse est incorrecte.

]]> #sol

]]> #bad1

]]> #bad2

]]> #bad3

]]> <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>x1</mi><mo>=</mo><mi>random</mi><mo>(</mo><mo>-</mo><mn>100</mn><mo>.</mo><mo>.</mo><mn>100</mn><mo>.</mo><mo>.</mo><mn>0</mn><mo>.</mo><mn>01</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>y1</mi><mo>=</mo><mi>random</mi><mo>(</mo><mo>-</mo><mn>100</mn><mo>.</mo><mo>.</mo><mn>100</mn><mo>.</mo><mo>.</mo><mn>0</mn><mo>.</mo><mn>01</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>a</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>10</mn><mo>.</mo><mo>.</mo><mn>10</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mrow><mn>0</mn><mo>,</mo><mn>1</mn></mrow></mfenced><mo>)</mo></mtd></mtr><mtr><mtd><mi>b</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>10</mn><mo>.</mo><mo>.</mo><mn>10</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mrow><mn>0</mn><mo>,</mo><mn>1</mn></mrow></mfenced><mo>)</mo></mtd></mtr><mtr><mtd><mi>bad1</mi><mo>=</mo><mi>a</mi><mo>*</mo><mfenced close="|" open="|"><mi>x1</mi></mfenced><mo>+</mo><mi>b</mi><mo>*</mo><mfenced close="|" open="|"><mi>y1</mi></mfenced></mtd></mtr><mtr><mtd><mi>sol</mi><mo>=</mo><mi>a</mi><mo>*</mo><mfenced close="⌋" open="⌊"><mi>x1</mi></mfenced><mo>+</mo><mi>b</mi><mo>*</mo><mfenced close="⌋" open="⌊"><mi>y1</mi></mfenced></mtd></mtr><mtr><mtd><mi>bad2</mi><mo>=</mo><mi>a</mi><mo>*</mo><mi>b</mi><mo>*</mo><mfenced close="⌋" open="⌊"><mrow><mi>x1</mi><mo>+</mo><mi>y1</mi></mrow></mfenced></mtd></mtr></mtable><mrow><mi>sol</mi><mo>≠</mo><mi>bad2</mi><mo>∧</mo><mi>sol</mi><mo>≠</mo><mi>bad1</mi></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad3</mi><mo>=</mo><mi>a</mi><mo>*</mo><mfenced close="⌉" open="⌈"><mi>x1</mi></mfenced><mo>+</mo><mi>b</mi><mo>*</mo><mfenced close="⌉" open="⌈"><mi>y1</mi></mfenced></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>28.62</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>76.07</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>10</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>9</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>964</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>970.83</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>9360</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>983</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><options><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option><option name="decimal_separator">,</option></options><localData><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data></localData></question> 0)]]> Quelle est la valeur de [#a] ?

]]> 4.0000000 0.3333333 0 0 #sol Votre réponse est exacte.

]]> #a Votre réponse est erronée. Vous n'avez pas donné la valeur du plus grand entier inférieur ou égal à #a.

]]> #sol+1]]> Votre réponse est erronée. Vous avez donné la valeur du plus petit entier supérieur ou égal à #a et non le plus grand entier inférieur ou égal à #a.

]]> 4.0000000 0.3333333 0 0 #sol]]> Vous avez une bonne réponse.

]]> #bad1]]> Votre réponse est erronée. Vous n'avez pas donné la valeur du plus grand entier inférieur ou égal à #a.

]]> #bad2]]> Votre réponse est erronée. Vous avez donné la valeur du plus petit entier supérieur ou égal à #a et non la valeur du plus grand entier inférieur ou égal à #a

]]> 4.0000000 0.3333333 0 0 #sol]]> Super! C'est la bonne réponse.

]]> #bad1]]> Désolé, vous n'avez pas donné la valeur du plus grand entier inférieur ou égal à #a.

]]> #bad2]]> Désolé, vous n'avez pas donné la valeur du plus grand entier inférieur ou égal à #a, mais le plus petit entier supérieur ou égal à #a.

]]> 4.0000000 0.3333333 0 0 #sol]]> Bonne réponse!

]]> #bad1]]> Désolé, vous n'avez pas donné la valeur du plus grand entier inférieur ou égal à «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msqrt»«mo»#«/mo»«mi»a«/mi»«/msqrt»«/math».

Portez une attention particulière à la fonction partie entière.

]]> #bad2]]> Désolé, vous n'avez pas donné la valeur du plus grand entier inférieur ou égal à «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msqrt»«mo»#«/mo»«mi»a«/mi»«/msqrt»«/math», mais le plus petit entier supérieur ou égal à «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msqrt»«mo»#«/mo»«mi»a«/mi»«/msqrt»«/math».

Portez une attention particulière à la fonction partie entière.

]]> 4.0000000 0.3333333 0 0 #sol]]> Bonne réponse!

]]> #bad1 Désolé, vous avez donné la valeur du plus grand entier inférieur ou égal à «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»a«/mi»«/math» et non le plus grand entier inférieur ou égal à «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«msup»«mi»a«/mi»«mn»2«/mn»«/msup»«/math».

]]> #bad2 Désolé, vous avez donné la valeur de «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«msup»«mi»a«/mi»«mn»2«/mn»«/msup»«/math» et non le plus grand entier inférieur ou égal à «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«msup»«mi»a«/mi»«mn»2«/mn»«/msup»«/math».

]]> #bad3 Désolé, vous avez donné la valeur du plus petit entier supérieur ou égal «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«msup»«mi»a«/mi»«mn»2«/mn»«/msup»«/math» et non le plus grand entier inférieur ou égal à «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«msup»«mi»a«/mi»«mn»2«/mn»«/msup»«/math».

Portez une attention particulière à votre compréhension de la fonction partie entière.

]]> 4.0000000 0.3333333 0 0 #sol]]> Votre réponse est exacte.

]]> #bad1 Votre réponse est erronée. Vous n'avez pas donné la valeur du plus grand entier inférieur ou égal à #a.

]]> #bad2 Votre réponse est erronée. Vous avez donné la valeur du plus petit entier supérieur ou égal à #a et non le plus grand entier inférieur ou égal à #a.

]]> 4.0000000 0.3333333 0 0 #sol]]> Bonne réponse!

]]> #bad1]]> Désolé, vous n'avez pas donné la valeur du plus grand entier inférieur ou égal à «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfenced open=¨[¨ close=¨]¨»«mrow»«mo»-«/mo»«msqrt»«mo»#«/mo»«mi»a«/mi»«/msqrt»«/mrow»«/mfenced»«/math» mais plutôt à «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»-«/mo»«msqrt»«mo»#«/mo»«mi»a«/mi»«/msqrt»«/math».

Portez une attention particulière à la fonction partie entière.

]]> #bad3]]> Désolé, votre réponse ne respecte pas la contrainte du domaine souhaité «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfenced open=¨[¨ close=¨]¨»«mrow»«mo»-«/mo»«mo»§#8734;«/mo»«mo»,«/mo»«mn»0«/mn»«/mrow»«/mfenced»«/math». Vous avez calculé «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfenced open=¨[¨ close=¨]¨»«msqrt»«mo»#«/mo»«mi»a«/mi»«/msqrt»«/mfenced»«/math» à la place de «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfenced open=¨[¨ close=¨]¨»«mrow»«mo»-«/mo»«msqrt»«mo»#«/mo»«mi»a«/mi»«/msqrt»«/mrow»«/mfenced»«/math».

]]> 4.0000000 0.3333333 0 0 #sol]]> Votre réponse est exacte.

]]> #bad1 Votre réponse est erronée. Vous n'avez pas donné la valeur du plus grand entier inférieur ou égal à #a.

]]> #bad2 Votre réponse est erronée. Vous avez donné la valeur du plus petit entier supérieur ou égal à #a et non le plus grand entier inférieur ou égal à #a.

]]> 4.0000000 0.3333333 0 0 #sol]]> Bonne réponse!

]]> #bad1 Désolé, vous avez donné la valeur du plus grand entier inférieur ou égal à «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»a«/mi»«/math» et non du plus grand entier inférieur ou égal à «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«msup»«mi»a«/mi»«mn»3«/mn»«/msup»«/math».

]]> #bad2 Désolé, vous avez donné la valeur de «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«msup»«mi»a«/mi»«mn»3«/mn»«/msup»«/math» et non le plus grand entier inférieur à «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«msup»«mi»a«/mi»«mn»3«/mn»«/msup»«/math».

]]> #bad3 Désolé, vous avez donné la valeur du plus petit entier supérieur ou égal à «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«msup»«mi»a«/mi»«mn»3«/mn»«/msup»«/math» et non du plus grand entier inférieur ou égal à «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«msup»«mi»a«/mi»«mn»3«/mn»«/msup»«/math».

Portez une attention particulière à votre compréhension de la fonction partie entière.

]]> 4.0000000 0.3333333 0 0 #sol]]> Bonne réponse!

]]> #bad1 Désolé, vous avez donné la valeur du plus grand entier inférieur ou égal à «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mo»#«/mo»«mi»a«/mi»«/mrow»«mn»3«/mn»«/mfrac»«/math» et non du plus grand entier inférieur ou égal à «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»-«/mo»«mfrac»«mrow»«mo»#«/mo»«mi»a«/mi»«/mrow»«mn»3«/mn»«/mfrac»«/math».

]]> #bad2 Désolé, vous avez donné la valeur de «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»-«/mo»«mfrac»«mrow»«mo»#«/mo»«mi»a«/mi»«/mrow»«mn»3«/mn»«/mfrac»«/math» et non le plus grand entier inférieur à «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»-«/mo»«mfrac»«mrow»«mo»#«/mo»«mi»a«/mi»«/mrow»«mn»3«/mn»«/mfrac»«/math».

]]> #bad3 Désolé, vous avez donné la valeur du plus petit entier supérieur ou égal à «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»-«/mo»«mfrac»«mrow»«mo»#«/mo»«mi»a«/mi»«/mrow»«mn»3«/mn»«/mfrac»«/math» et non du plus grand entier inférieur ou égal à «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»-«/mo»«mfrac»«mrow»«mo»#«/mo»«mi»a«/mi»«/mrow»«mn»3«/mn»«/mfrac»«/math».

#plotter1

]]> La règle utilisée pour ce graphique est: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»y«/mi»«mo»=«/mo»«mo»#«/mo»«mi»a«/mi»«mo»§#183;«/mo»«mo»[«/mo»«mo»#«/mo»«mi»b«/mi»«mo»§#183;«/mo»«mo»(«/mo»«mi»x«/mi»«mo»-«/mo»«mo»#«/mo»«mi»h«/mi»«mo»)«/mo»«mo»]«/mo»«mo»+«/mo»«mo»#«/mo»«mi»k«/mi»«/math». Infinité de réponses possibles.

]]> 1.0000000 0.3333333 0 0 a=#solab=#solbh=#solhk=#solk]]> <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Paramètres</mi><mo> </mo><mi>de</mi><mo> </mo><mi>la</mi><mo> </mo><mi>fonction</mi><mo> </mo><mi>partie</mi><mo> </mo><mi>entère</mi><mo> </mo><mi>à</mi><mo> </mo><mi>l</mi><mo>'</mo><mi>étude</mi></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mn>2</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mn>2</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mo>=</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k</mi><mo>=</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>random</mi><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>1</mn><mo>/</mo><mn>5</mn><mo>,</mo><mn>1</mn><mo>/</mo><mn>3</mn><mo>,</mo><mn>1</mn><mo>/</mo><mn>3</mn><mo>,</mo><mn>1</mn><mo>/</mo><mn>2</mn><mo>,</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>3</mn></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Paramétrage</mi><mo> </mo><mi>de</mi><mo> </mo><mi>la</mi><mo> </mo><mi>fenêtre</mi><mo> </mo><mi>d</mi><mo>'</mo><mi>affichage</mi></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>WH</mi><mo>=</mo><mn>500</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>WW</mi><mo>=</mo><mn>500</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w1</mi><mo>:</mo><mo>=</mo><mi>show_axis</mi><mo>=</mo><mi>true</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w2</mi><mo>:</mo><mo>=</mo><mi>show_grid</mi><mo>=</mo><mi>true</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w3</mi><mo>:</mo><mo>=</mo><mi>window_height</mi><mo>=</mo><mi>WH</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w4</mi><mo>:</mo><mo>=</mo><mi>window_width</mi><mo>=</mo><mi>WW</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w5</mi><mo>:</mo><mo>=</mo><mi>window_aspect_ratio</mi><mo>=</mo><mi>WH</mi><mo>/</mo><mi>WW</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w6</mi><mo>:</mo><mo>=</mo><mi>axis_color</mi><mo>=</mo><mi>black</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w7</mi><mo>:</mo><mo>=</mo><mi>grid_color</mi><mo>=</mo><mi>green</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w8</mi><mo>:</mo><mo>=</mo><mi>axis_style</mi><mo>=</mo><mo>"</mo><mi>arrow_xy</mi><mo>"</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w9</mi><mo>:</mo><mo>=</mo><mi>axis_label</mi><mo>=</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>"</mo><mi>x</mi><mo>"</mo><mo>,</mo><mo>"</mo><mi>y</mi><mo> </mo><mo>"</mo></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo>=</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>w1</mi><mo>,</mo><mi>w2</mi><mo>,</mo><mi>w3</mi><mo>,</mo><mi>w4</mi><mo>,</mo><mi>w5</mi><mo>,</mo><mi>w6</mi><mo>,</mo><mi>w7</mi><mo>,</mo><mi>w8</mi><mo>,</mo><mi>w9</mi><mo>,</mo><mi>grid_step_x</mi><mo>=</mo><mn>1</mn><mo>/</mo><mi>b</mi><mo>,</mo><mo> </mo><mi>grid_step_y</mi><mo>=</mo><mi>a</mi></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>L</mi><mo>=</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd/></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Lg</mi><mo>=</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd/></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Ld</mi><mo>=</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd/></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Ldb</mi><mo>=</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd/></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">for</csymbol><mrow><mi>i</mi><mo> </mo><mi>in</mi><mo> </mo><mo>-</mo><mn>10</mn><mo>.</mo><mo>.</mo><mn>10</mn></mrow><mtable><mtr><mtd><mi>L</mi><mo>=</mo><mi>append</mi><mo>(</mo><mi>L</mi><mo>,</mo><mi>segment</mi><mo>(</mo><mi>point</mi><mo>(</mo><mi>i</mi><mo>/</mo><mi>b</mi><mo>+</mo><mi>h</mi><mo>,</mo><mi>i</mi><mo>*</mo><mi>a</mi><mo>+</mo><mi>k</mi><mo>)</mo><mo>,</mo><mi>point</mi><mo>(</mo><mfenced><mrow><mi>i</mi><mo>+</mo><mn>1</mn></mrow></mfenced><mo>/</mo><mi>b</mi><mo>+</mo><mi>h</mi><mo>,</mo><mi>i</mi><mo>*</mo><mi>a</mi><mo>+</mo><mi>k</mi><mo>)</mo><mo>)</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>Lg</mi><mo>=</mo><mi>append</mi><mo>(</mo><mi>Lg</mi><mo>,</mo><mi>point</mi><mo>(</mo><mi>i</mi><mo>/</mo><mi>b</mi><mo>+</mo><mi>h</mi><mo>,</mo><mi>i</mi><mo>*</mo><mi>a</mi><mo>+</mo><mi>k</mi><mo>)</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>Ld</mi><mo>=</mo><mi>append</mi><mo>(</mo><mi>Ld</mi><mo>,</mo><mi>point</mi><mo>(</mo><mfenced><mrow><mi>i</mi><mo>+</mo><mn>1</mn></mrow></mfenced><mo>/</mo><mi>b</mi><mo>+</mo><mi>h</mi><mo>,</mo><mi>i</mi><mo>*</mo><mi>a</mi><mo>+</mo><mi>k</mi><mo>)</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>Ldb</mi><mo>=</mo><mi>append</mi><mo>(</mo><mi>Ldb</mi><mo>,</mo><mi>point</mi><mo>(</mo><mfenced><mrow><mi>i</mi><mo>+</mo><mn>1</mn></mrow></mfenced><mo>/</mo><mi>b</mi><mo>+</mo><mi>h</mi><mo>,</mo><mi>i</mi><mo>*</mo><mi>a</mi><mo>+</mo><mi>k</mi><mo>)</mo><mo>)</mo></mtd></mtr></mtable></apply></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Préparation</mi><mo> </mo><mi>du</mi><mo> </mo><mi>graphique</mi></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tr</mi><mo>=</mo><mi>plotter</mi><mo>(</mo><mi>point</mi><mo>(</mo><mi>h</mi><mo>-</mo><mn>2</mn><mo>,</mo><mi>k</mi><mo>-</mo><mn>2</mn><mo>)</mo><mo>,</mo><mn>10</mn><mo>/</mo><mi>b</mi><mo>+</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>*</mo><mi>a</mi><mo>+</mo><mn>1</mn><mo>,</mo><mi>W</mi><mo>)</mo></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Traçage</mi><mo> </mo><mi>des</mi><mo> </mo><mi>segments</mi></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>plot</mi><mo>(</mo><mi>tr</mi><mo>,</mo><mi>L</mi><mo>)</mo></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Points</mi><mo> </mo><mi>aux</mi><mo> </mo><mi>extrémités</mi></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>plot</mi><mo>(</mo><mi>tr</mi><mo>,</mo><mi>Lg</mi><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>point_size</mi><mo>=</mo><mn>6</mn><mo>,</mo><mi>color</mi><mo>=</mo><mi>blue</mi></mtd></mtr></mtable></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>plot</mi><mo>(</mo><mi>tr</mi><mo>,</mo><mi>Ld</mi><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>point_size</mi><mo>=</mo><mn>6</mn><mo>,</mo><mi>color</mi><mo>=</mo><mi>blue</mi></mtd></mtr></mtable></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>plot</mi><mo>(</mo><mi>tr</mi><mo>,</mo><mi>Ldb</mi><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>point_size</mi><mo>=</mo><mn>4</mn><mo>,</mo><mi>color</mi><mo>=</mo><mi>white</mi></mtd></mtr></mtable></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>credit</mi><mo>=</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>credit1</mi><mo>=</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>credit2</mi><mo>=</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>credit3</mi><mo>=</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>fg</mi><mo>(</mo><mi>a1</mi><mo>,</mo><mi>b1</mi><mo>,</mo><mi>h1</mi><mo>,</mo><mi>k1</mi><mo>)</mo><mo>:</mo><mo>=</mo><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">begin</csymbol><mtable><mtr><mtd><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mfenced><mrow><mi>a1</mi><mo>=</mo><mi>a</mi></mrow></mfenced><mo>∧</mo><mfenced><mrow><mi>b1</mi><mo>=</mo><mi>b</mi></mrow></mfenced></mrow><mrow><mi>credit1</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>5</mn></mrow></apply></mtd></mtr><mtr><mtd><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>credit1</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>5</mn><mo>∧</mo><mfenced><mrow><mfenced><mrow><mi>h1</mi><mo>-</mo><mi>h</mi></mrow></mfenced><mo>/</mo><mo>(</mo><mn>1</mn><mo>/</mo><mi>b</mi><mo>)</mo></mrow></mfenced><mo>∈</mo><integers/></mrow><mrow><mi>credit2</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>25</mn></mrow></apply></mtd></mtr><mtr><mtd><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>credit1</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>5</mn><mo>∧</mo><mfenced><mrow><mfenced><mrow><mi>k1</mi><mo>-</mo><mi>k</mi></mrow></mfenced><mo>/</mo><mi>a</mi></mrow></mfenced><mo>∈</mo><integers/></mrow><mrow><mi>credit3</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>25</mn></mrow></apply></mtd></mtr><mtr><mtd><mi>credit</mi><mo>=</mo><mi>credit1</mi><mo>+</mo><mi>credit2</mi><mo>+</mo><mi>credit3</mi></mtd></mtr><mtr><mtd><mi>return</mi><mo> </mo><mi>credit</mi></mtd></mtr></mtable></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sola</mi><mo>=</mo><mi>a</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>solb</mi><mo>=</mo><mi>b</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>solh</mi><mo>=</mo><mi>h</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>solk</mi><mo>=</mo><mi>k</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>1</mn><mn>2</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tt</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mo>#</mo><mi>s</mi><mi>o</mi><mi>l</mi><mi>a</mi><mspace linebreak="newline"/><mi>b</mi><mo>=</mo><mo>#</mo><mi>s</mi><mi>o</mi><mi>l</mi><mi>b</mi><mspace linebreak="newline"/><mi>h</mi><mo>=</mo><mo>#</mo><mi>s</mi><mi>o</mi><mi>l</mi><mi>h</mi><mspace linebreak="newline"/><mi>k</mi><mo>=</mo><mo>#</mo><mi>s</mi><mi>o</mi><mi>l</mi><mi>k</mi><mspace linebreak="newline"/><mspace linebreak="newline"/><mspace linebreak="newline"/><mspace linebreak="newline"/><mspace linebreak="newline"/><mspace linebreak="newline"/><mspace linebreak="newline"/></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"><param name="itemseparators">;, \n</param><param name="decimalseparators">., \,</param></assertion><assertion name="equivalent_function"><param name="name">fg</param><param name="notevaluate">false</param></assertion></assertions><options><option name="tolerance">0.001</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option><option name="decimal_separator">,</option></options><localData><data name="inputField">popupEditor</data><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="inputCompound">true</data></localData></question> Partie_entière_graphique_wiris Détermine les paramètres a, b, h et k de la fonction partie entière représentée «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfenced»«mrow»«mi»y«/mi»«mo»=«/mo»«mi»a«/mi»«mo»[«/mo»«mi»b«/mi»«mo»(«/mo»«mi»x«/mi»«mo»-«/mo»«mi»h«/mi»«mo»)«/mo»«mo»]«/mo»«mo»+«/mo»«mi»k«/mi»«/mrow»«/mfenced»«/math». Les paramètres h et k doivent être des nombres entiers.

#plotter1

]]> 1.0000000 0.3333333 0 0 a=#solab=#solbh=#solhk=#solk]]> <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Paramètres</mi><mo> </mo><mi>de</mi><mo> </mo><mi>la</mi><mo> </mo><mi>fonction</mi><mo> </mo><mi>partie</mi><mo> </mo><mi>entère</mi><mo> </mo><mi>à</mi><mo> </mo><mi>l</mi><mo>'</mo><mi>étude</mi></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mn>2</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mn>2</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mo>=</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k</mi><mo>=</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>random</mi><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>1</mn><mo>/</mo><mn>5</mn><mo>,</mo><mn>1</mn><mo>/</mo><mn>3</mn><mo>,</mo><mn>1</mn><mo>/</mo><mn>3</mn><mo>,</mo><mn>1</mn><mo>/</mo><mn>2</mn><mo>,</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>3</mn></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Paramétrage</mi><mo> </mo><mi>de</mi><mo> </mo><mi>la</mi><mo> </mo><mi>fenêtre</mi><mo> </mo><mi>d</mi><mo>'</mo><mi>affichage</mi></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>WH</mi><mo>=</mo><mn>500</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>WW</mi><mo>=</mo><mn>500</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w1</mi><mo>:</mo><mo>=</mo><mi>show_axis</mi><mo>=</mo><mi>true</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w2</mi><mo>:</mo><mo>=</mo><mi>show_grid</mi><mo>=</mo><mi>true</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w3</mi><mo>:</mo><mo>=</mo><mi>window_height</mi><mo>=</mo><mi>WH</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w4</mi><mo>:</mo><mo>=</mo><mi>window_width</mi><mo>=</mo><mi>WW</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w5</mi><mo>:</mo><mo>=</mo><mi>window_aspect_ratio</mi><mo>=</mo><mi>WH</mi><mo>/</mo><mi>WW</mi></math></input></command><command><input><math 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align="center"><mtr><mtd><mi>w1</mi><mo>,</mo><mi>w2</mi><mo>,</mo><mi>w3</mi><mo>,</mo><mi>w4</mi><mo>,</mo><mi>w5</mi><mo>,</mo><mi>w6</mi><mo>,</mo><mi>w7</mi><mo>,</mo><mi>w8</mi><mo>,</mo><mi>w9</mi><mo>,</mo><mi>grid_step_x</mi><mo>=</mo><mn>1</mn><mo>/</mo><mi>b</mi><mo>,</mo><mo> </mo><mi>grid_step_y</mi><mo>=</mo><mi>a</mi></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>L</mi><mo>=</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd/></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Lg</mi><mo>=</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd/></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Ld</mi><mo>=</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd/></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Ldb</mi><mo>=</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd/></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">for</csymbol><mrow><mi>i</mi><mo> </mo><mi>in</mi><mo> </mo><mo>-</mo><mn>10</mn><mo>.</mo><mo>.</mo><mn>10</mn></mrow><mtable><mtr><mtd><mi>L</mi><mo>=</mo><mi>append</mi><mo>(</mo><mi>L</mi><mo>,</mo><mi>segment</mi><mo>(</mo><mi>point</mi><mo>(</mo><mi>i</mi><mo>/</mo><mi>b</mi><mo>+</mo><mi>h</mi><mo>,</mo><mi>i</mi><mo>*</mo><mi>a</mi><mo>+</mo><mi>k</mi><mo>)</mo><mo>,</mo><mi>point</mi><mo>(</mo><mfenced><mrow><mi>i</mi><mo>+</mo><mn>1</mn></mrow></mfenced><mo>/</mo><mi>b</mi><mo>+</mo><mi>h</mi><mo>,</mo><mi>i</mi><mo>*</mo><mi>a</mi><mo>+</mo><mi>k</mi><mo>)</mo><mo>)</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>Lg</mi><mo>=</mo><mi>append</mi><mo>(</mo><mi>Lg</mi><mo>,</mo><mi>point</mi><mo>(</mo><mi>i</mi><mo>/</mo><mi>b</mi><mo>+</mo><mi>h</mi><mo>,</mo><mi>i</mi><mo>*</mo><mi>a</mi><mo>+</mo><mi>k</mi><mo>)</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>Ld</mi><mo>=</mo><mi>append</mi><mo>(</mo><mi>Ld</mi><mo>,</mo><mi>point</mi><mo>(</mo><mfenced><mrow><mi>i</mi><mo>+</mo><mn>1</mn></mrow></mfenced><mo>/</mo><mi>b</mi><mo>+</mo><mi>h</mi><mo>,</mo><mi>i</mi><mo>*</mo><mi>a</mi><mo>+</mo><mi>k</mi><mo>)</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>Ldb</mi><mo>=</mo><mi>append</mi><mo>(</mo><mi>Ldb</mi><mo>,</mo><mi>point</mi><mo>(</mo><mfenced><mrow><mi>i</mi><mo>+</mo><mn>1</mn></mrow></mfenced><mo>/</mo><mi>b</mi><mo>+</mo><mi>h</mi><mo>,</mo><mi>i</mi><mo>*</mo><mi>a</mi><mo>+</mo><mi>k</mi><mo>)</mo><mo>)</mo></mtd></mtr></mtable></apply></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Préparation</mi><mo> </mo><mi>du</mi><mo> </mo><mi>graphique</mi></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tr</mi><mo>=</mo><mi>plotter</mi><mo>(</mo><mi>point</mi><mo>(</mo><mi>h</mi><mo>-</mo><mn>2</mn><mo>,</mo><mi>k</mi><mo>-</mo><mn>2</mn><mo>)</mo><mo>,</mo><mn>10</mn><mo>/</mo><mi>b</mi><mo>+</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>*</mo><mi>a</mi><mo>+</mo><mn>1</mn><mo>,</mo><mi>W</mi><mo>)</mo></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Traçage</mi><mo> </mo><mi>des</mi><mo> </mo><mi>segments</mi></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>plot</mi><mo>(</mo><mi>tr</mi><mo>,</mo><mi>L</mi><mo>)</mo></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Points</mi><mo> </mo><mi>aux</mi><mo> </mo><mi>extrémités</mi></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>plot</mi><mo>(</mo><mi>tr</mi><mo>,</mo><mi>Lg</mi><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>point_size</mi><mo>=</mo><mn>6</mn><mo>,</mo><mi>color</mi><mo>=</mo><mi>blue</mi></mtd></mtr></mtable></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>plot</mi><mo>(</mo><mi>tr</mi><mo>,</mo><mi>Ld</mi><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>point_size</mi><mo>=</mo><mn>6</mn><mo>,</mo><mi>color</mi><mo>=</mo><mi>blue</mi></mtd></mtr></mtable></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>plot</mi><mo>(</mo><mi>tr</mi><mo>,</mo><mi>Ldb</mi><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>point_size</mi><mo>=</mo><mn>4</mn><mo>,</mo><mi>color</mi><mo>=</mo><mi>white</mi></mtd></mtr></mtable></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>credit</mi><mo>=</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>credit1</mi><mo>=</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>credit2</mi><mo>=</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>credit3</mi><mo>=</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>fg</mi><mo>(</mo><mi>a1</mi><mo>,</mo><mi>b1</mi><mo>,</mo><mi>h1</mi><mo>,</mo><mi>k1</mi><mo>)</mo><mo>:</mo><mo>=</mo><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">begin</csymbol><mtable><mtr><mtd><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mfenced><mrow><mi>a1</mi><mo>=</mo><mi>a</mi></mrow></mfenced><mo>∧</mo><mfenced><mrow><mi>b1</mi><mo>=</mo><mi>b</mi></mrow></mfenced></mrow><mrow><mi>credit1</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>5</mn></mrow></apply></mtd></mtr><mtr><mtd><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>credit1</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>5</mn><mo>∧</mo><mfenced><mrow><mfenced><mrow><mi>h1</mi><mo>-</mo><mi>h</mi></mrow></mfenced><mo>/</mo><mo>(</mo><mn>1</mn><mo>/</mo><mi>b</mi><mo>)</mo></mrow></mfenced><mo>∈</mo><integers/></mrow><mrow><mi>credit2</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>25</mn></mrow></apply></mtd></mtr><mtr><mtd><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>credit1</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>5</mn><mo>∧</mo><mfenced><mrow><mfenced><mrow><mi>k1</mi><mo>-</mo><mi>k</mi></mrow></mfenced><mo>/</mo><mi>a</mi></mrow></mfenced><mo>∈</mo><integers/></mrow><mrow><mi>credit3</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>25</mn></mrow></apply></mtd></mtr><mtr><mtd><mi>credit</mi><mo>=</mo><mi>credit1</mi><mo>+</mo><mi>credit2</mi><mo>+</mo><mi>credit3</mi></mtd></mtr><mtr><mtd><mi>return</mi><mo> </mo><mi>credit</mi></mtd></mtr></mtable></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sola</mi><mo>=</mo><mi>a</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>solb</mi><mo>=</mo><mi>b</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>solh</mi><mo>=</mo><mi>h</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>solk</mi><mo>=</mo><mi>k</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>1</mn><mn>2</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tt</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mo>#</mo><mi>s</mi><mi>o</mi><mi>l</mi><mi>a</mi><mspace linebreak="newline"/><mi>b</mi><mo>=</mo><mo>#</mo><mi>s</mi><mi>o</mi><mi>l</mi><mi>b</mi><mspace linebreak="newline"/><mi>h</mi><mo>=</mo><mo>#</mo><mi>s</mi><mi>o</mi><mi>l</mi><mi>h</mi><mspace linebreak="newline"/><mi>k</mi><mo>=</mo><mo>#</mo><mi>s</mi><mi>o</mi><mi>l</mi><mi>k</mi><mspace linebreak="newline"/><mspace linebreak="newline"/><mspace linebreak="newline"/><mspace linebreak="newline"/><mspace linebreak="newline"/><mspace linebreak="newline"/><mspace linebreak="newline"/></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"><param name="itemseparators">;, \n</param><param name="decimalseparators">., \,</param></assertion><assertion name="equivalent_function"><param name="name">fg</param><param name="notevaluate">false</param></assertion></assertions><options><option name="tolerance">0.001</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="inputCompound">true</data></localData></question> $course$/top/CSSBE/Sec 4/Fonctions/2.1 - Propriétés d'une fonction $course$/top/CSSBE/Sec 4/Fonctions/2.1 - Propriétés d'une fonction/2.1.3 - Ordonnée et abscisse à l'origine Domaine_fonction_parties-1 Quel est le domaine de la fonction représentée ci-dessous?

Domaine: {#1}{#2},{#3}{#4}

#plotter1

]]> 4.0000000 0.3333333 0 <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Paramétrage</mi><mo> </mo><mi>du</mi><mo> </mo><mi>plan</mi><mo> </mo><mi>cartésien</mi><mo> </mo><mi>utilisé</mi></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>WH</mi><mo>=</mo><mn>500</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>WW</mi><mo>=</mo><mn>500</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w1</mi><mo>:</mo><mo>=</mo><mi>show_axis</mi><mo>=</mo><mi>true</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w2</mi><mo>:</mo><mo>=</mo><mi>show_grid</mi><mo>=</mo><mi>true</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w3</mi><mo>:</mo><mo>=</mo><mi>window_height</mi><mo>=</mo><mi>WH</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w4</mi><mo>:</mo><mo>=</mo><mi>window_width</mi><mo>=</mo><mi>WW</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w5</mi><mo>:</mo><mo>=</mo><mi>window_aspect_ratio</mi><mo>=</mo><mi>WH</mi><mo>/</mo><mi>WW</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w6</mi><mo>:</mo><mo>=</mo><mi>axis_color</mi><mo>=</mo><mi>black</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w7</mi><mo>:</mo><mo>=</mo><mi>grid_color</mi><mo>=</mo><mi>green</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w8</mi><mo>:</mo><mo>=</mo><mi>axis_style</mi><mo>=</mo><mo>"</mo><mi>arrow_xy</mi><mo>"</mo></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w9</mi><mo>:</mo><mo>=</mo><mi>axis_label</mi><mo>=</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>"</mo><mi>Le</mi><mo> </mo><mi>fonctionnement</mi><mo> </mo><mi>du</mi><mo> </mo><mi>moteur</mi><mo> </mo><mi>en</mi><mo> </mo><mi>secondes</mi><mo> </mo><mo> </mo><mo>"</mo><mo>,</mo><mo>"</mo><mi>L</mi><mo>'</mo><mi>altitude</mi><mo> </mo><mi>en</mi><mo> </mo><mi>mètres</mi><mo> </mo><mo> </mo><mo> </mo><mo>"</mo></mtd></mtr></mtable></mfenced></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo>=</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>w1</mi><mo>,</mo><mi>w2</mi><mo>,</mo><mi>w3</mi><mo>,</mo><mi>w4</mi><mo>,</mo><mi>w5</mi><mo>,</mo><mi>w6</mi><mo>,</mo><mi>w7</mi><mo>,</mo><mi>w8</mi></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>On</mi><mo> </mo><mi>détermine</mi><mo> </mo><mi>où</mi><mo> </mo><mi>la</mi><mo> </mo><mi>quadratique</mi><mo> </mo><mi>va</mi><mo> </mo><mi>changer</mi><mo> </mo><mi>pour</mi><mo> </mo><mi>constante</mi><mo> </mo><mi>avec</mi><mo> </mo><mo>"</mo><mi>a</mi><mo>"</mo></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Définition</mi><mo> </mo><mi>des</mi><mo> </mo><mi>fonctions</mi></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><msup><mi>x</mi><mn>2</mn></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><msup><mi>a</mi><mn>2</mn></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><mn>2</mn><mo>*</mo><mi>x</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Définition</mi><mo> </mo><mi>du</mi><mo> </mo><mi>plan</mi><mo> </mo><mi>de</mi><mo> </mo><mi>travail</mi><mo> </mo><mi>en</mi><mo> </mo><mi>tenant</mi><mo> </mo><mi>compte</mi><mo> </mo><mi>de</mi><mo> </mo><mi>a</mi><mo> </mo><mi>et</mi><mo> </mo><mi>de</mi><mo> </mo><msup><mi>a</mi><mrow><mn>2</mn><mo> </mo></mrow></msup><mi>pour</mi><mo> </mo><mi>les</mi><mo> </mo><mi>valeurs</mi><mo> </mo><mi>de</mi><mo> </mo><mo>"</mo><mi>y</mi><mo>"</mo></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tr</mi><mo>=</mo><mi>plotter</mi><mo>(</mo><mi>point</mi><mfenced><mrow><mn>0</mn><mo>,</mo><mn>0</mn></mrow></mfenced><mo>,</mo><mn>21</mn><mo>,</mo><mn>2</mn><msup><mi>a</mi><mn>2</mn></msup><mo>+</mo><mn>5</mn><mo>,</mo><mi>W</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>On</mi><mo> </mo><mi>trace</mi><mo> </mo><mi>les</mi><mo> </mo><mi>fonctions</mi><mo> </mo><mi>avec</mi><mo> </mo><mi>limite</mi><mo> </mo><mi>la</mi><mo> </mo><mi>valeur</mi><mo> </mo><mi>de</mi><mo> </mo><mo>"</mo><mi>a</mi><mo>"</mo></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>plot</mi><mo>(</mo><mi>f</mi><mo>,</mo><mn>0</mn><mo>.</mo><mo>.</mo><mi>a</mi><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>line_width</mi><mo>=</mo><mn>2</mn><mo>,</mo><mi>color</mi><mo>=</mo><mi>blue</mi></mtd></mtr></mtable></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>plot</mi><mo>(</mo><mi>g</mi><mo>,</mo><mi>a</mi><mo>.</mo><mo>.</mo><mi>a</mi><mo>+</mo><mn>4</mn><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>line_width</mi><mo>=</mo><mn>2</mn><mo>,</mo><mi>color</mi><mo>=</mo><mi>blue</mi></mtd></mtr></mtable></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>plot</mi><mo>(</mo><mi>h</mi><mo>,</mo><mn>0</mn><mo>.</mo><mo>.</mo><mo>-</mo><mi>a</mi><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>line_width</mi><mo>=</mo><mn>2</mn><mo>,</mo><mi>color</mi><mo>=</mo><mi>blue</mi></mtd></mtr></mtable></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Attribut</mi><mo> </mo><mi>graphique</mi><mo> </mo><mi>pour</mi><mo> </mo><mi>point</mi><mo> </mo><mi>ouvert</mi><mo> </mo><mi>en</mi><mo> </mo><mi>randomisant</mi><mo> </mo><mi>avec</mi><mo> </mo><mi>i</mi><mo> </mo><mi>et</mi><mo> </mo><mi>j</mi></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>j</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mrow><mi>PO1</mi><mo>=</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>point_size</mi><mo>=</mo><mn>6</mn><mo>,</mo><mi>color</mi><mo>=</mo><mi>red</mi></mtd></mtr></mtable></mfenced></mrow><mrow><mi>PO1</mi><mo>=</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>point_size</mi><mo>=</mo><mn>6</mn><mo>,</mo><mi>color</mi><mo>=</mo><mi>white</mi></mtd></mtr></mtable></mfenced></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>j</mi><mo>=</mo><mn>1</mn></mrow><mrow><mi>PO2</mi><mo>=</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>point_size</mi><mo>=</mo><mn>6</mn><mo>,</mo><mi>color</mi><mo>=</mo><mi>red</mi></mtd></mtr></mtable></mfenced></mrow><mrow><mi>PO2</mi><mo>=</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>point_size</mi><mo>=</mo><mn>6</mn><mo>,</mo><mi>color</mi><mo>=</mo><mi>white</mi></mtd></mtr></mtable></mfenced></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Bonne</mi><mo> </mo><mi>réponse</mi><mo> </mo><mi>en</mi><mo> </mo><mi>fonction</mi><mo> </mo><mi>de</mi><mo> </mo><mi>i</mi><mo> </mo><mi>et</mi><mo> </mo><mi>j</mi></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>i</mi><mo>=</mo><mn>1</mn><mo>∧</mo><mi>j</mi><mo>=</mo><mn>1</mn></mrow><mtable><mtr><mtd><mi>o1</mi><mo>=</mo><mo>"</mo><mo>[</mo><mo>"</mo></mtd></mtr><mtr><mtd><mi>a1</mi><mo>=</mo><mo>-</mo><mi>a</mi></mtd></mtr><mtr><mtd><mi>b</mi><mo>=</mo><mi>a</mi><mo>+</mo><mn>4</mn></mtd></mtr><mtr><mtd><mi>o2</mi><mo>=</mo><mo>"</mo><mo>]</mo><mo>"</mo></mtd></mtr></mtable><mrow><mi>i</mi><mo>=</mo><mn>1</mn><mo>∧</mo><mi>j</mi><mo>=</mo><mn>2</mn></mrow><mtable><mtr><mtd><mi>o1</mi><mo>=</mo><mo>"</mo><mo>[</mo><mo>"</mo></mtd></mtr><mtr><mtd><mi>a1</mi><mo>=</mo><mo>-</mo><mi>a</mi></mtd></mtr><mtr><mtd><mi>b</mi><mo>=</mo><mi>a</mi><mo>+</mo><mn>4</mn></mtd></mtr><mtr><mtd><mi>o2</mi><mo>=</mo><mo>"</mo><mo>[</mo><mo>"</mo></mtd></mtr></mtable><mrow><mi>i</mi><mo>=</mo><mn>2</mn><mo>∧</mo><mi>j</mi><mo>=</mo><mn>1</mn></mrow><mtable><mtr><mtd><mi>o1</mi><mo>=</mo><mo>"</mo><mo>]</mo><mo>"</mo></mtd></mtr><mtr><mtd><mi>a1</mi><mo>=</mo><mo>-</mo><mi>a</mi></mtd></mtr><mtr><mtd><mi>b</mi><mo>=</mo><mi>a</mi><mo>+</mo><mn>4</mn></mtd></mtr><mtr><mtd><mi>o2</mi><mo>=</mo><mo>"</mo><mo>]</mo><mo>"</mo></mtd></mtr></mtable><mtable><mtr><mtd><mi>o1</mi><mo>=</mo><mo>"</mo><mo>]</mo><mo>"</mo></mtd></mtr><mtr><mtd><mi>a1</mi><mo>=</mo><mo>-</mo><mi>a</mi></mtd></mtr><mtr><mtd><mi>b</mi><mo>=</mo><mi>a</mi><mo>+</mo><mn>4</mn></mtd></mtr><mtr><mtd><mi>o2</mi><mo>=</mo><mo>"</mo><mo>[</mo><mo>"</mo></mtd></mtr></mtable></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Astuce</mi><mo> </mo><mi>pour</mi><mo> </mo><mi>faire</mi><mo> </mo><mi>un</mi><mo> </mo><mi>point</mi><mo> </mo><mi>ouvert</mi></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>plot</mi><mo>(</mo><mi>point</mi><mo>(</mo><mo>-</mo><mi>a</mi><mo>,</mo><mi>h</mi><mo>(</mo><mo>-</mo><mi>a</mi><mo>)</mo><mo>)</mo><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>point_size</mi><mo>=</mo><mn>8</mn><mo>,</mo><mi>color</mi><mo>=</mo><mi>red</mi></mtd></mtr></mtable></mfenced><mo>)</mo></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>plot</mi><mo>(</mo><mi>point</mi><mo>(</mo><mo>-</mo><mi>a</mi><mo>,</mo><mi>h</mi><mo>(</mo><mo>-</mo><mi>a</mi><mo>)</mo><mo>)</mo><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>point_size</mi><mo>=</mo><mn>6</mn><mo>,</mo><mi>color</mi><mo>=</mo><mi>white</mi></mtd></mtr></mtable></mfenced><mo>)</mo></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>plot</mi><mo>(</mo><mi>point</mi><mo>(</mo><mo>-</mo><mi>a</mi><mo>,</mo><mi>h</mi><mo>(</mo><mo>-</mo><mi>a</mi><mo>)</mo><mo>)</mo><mo>,</mo><mi>PO1</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>plot</mi><mo>(</mo><mi>point</mi><mo>(</mo><mi>a</mi><mo>+</mo><mn>4</mn><mo>,</mo><msup><mi>a</mi><mn>2</mn></msup><mo>)</mo><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>point_size</mi><mo>=</mo><mn>8</mn><mo>,</mo><mi>color</mi><mo>=</mo><mi>red</mi></mtd></mtr></mtable></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>plot</mi><mo>(</mo><mi>point</mi><mo>(</mo><mi>a</mi><mo>+</mo><mn>4</mn><mo>,</mo><msup><mi>a</mi><mn>2</mn></msup><mo>)</mo><mo>,</mo><mi>PO2</mi><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>j</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>8</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>o1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><ms>]</ms></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>o2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><ms>[</ms></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">0.001</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data></localData></question> Domaine d'une fonction-par_parties Quel est le domaine de la fonction représentée ci-dessous ?

#plotter1

]]> 4.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Paramétrage</mi><mo> </mo><mi>du</mi><mo> </mo><mi>plan</mi><mo> </mo><mi>cartésien</mi><mo> </mo><mi>utilisé</mi></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>WH</mi><mo>=</mo><mn>500</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>WW</mi><mo>=</mo><mn>500</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w1</mi><mo>:</mo><mo>=</mo><mi>show_axis</mi><mo>=</mo><mi>true</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w2</mi><mo>:</mo><mo>=</mo><mi>show_grid</mi><mo>=</mo><mi>true</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w3</mi><mo>:</mo><mo>=</mo><mi>window_height</mi><mo>=</mo><mi>WH</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w4</mi><mo>:</mo><mo>=</mo><mi>window_width</mi><mo>=</mo><mi>WW</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w5</mi><mo>:</mo><mo>=</mo><mi>window_aspect_ratio</mi><mo>=</mo><mi>WH</mi><mo>/</mo><mi>WW</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w6</mi><mo>:</mo><mo>=</mo><mi>axis_color</mi><mo>=</mo><mi>black</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w7</mi><mo>:</mo><mo>=</mo><mi>grid_color</mi><mo>=</mo><mi>green</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w8</mi><mo>:</mo><mo>=</mo><mi>axis_style</mi><mo>=</mo><mo>"</mo><mi>arrow_xy</mi><mo>"</mo></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w9</mi><mo>:</mo><mo>=</mo><mi>axis_label</mi><mo>=</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>"</mo><mi>Le</mi><mo> </mo><mi>fonctionnement</mi><mo> </mo><mi>du</mi><mo> </mo><mi>moteur</mi><mo> </mo><mi>en</mi><mo> </mo><mi>secondes</mi><mo> </mo><mo> </mo><mo>"</mo><mo>,</mo><mo>"</mo><mi>L</mi><mo>'</mo><mi>altitude</mi><mo> </mo><mi>en</mi><mo> </mo><mi>mètres</mi><mo> </mo><mo> </mo><mo> </mo><mo>"</mo></mtd></mtr></mtable></mfenced></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo>=</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>w1</mi><mo>,</mo><mi>w2</mi><mo>,</mo><mi>w3</mi><mo>,</mo><mi>w4</mi><mo>,</mo><mi>w5</mi><mo>,</mo><mi>w6</mi><mo>,</mo><mi>w7</mi><mo>,</mo><mi>w8</mi></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>On</mi><mo> </mo><mi>détermine</mi><mo> </mo><mi>où</mi><mo> </mo><mi>la</mi><mo> </mo><mi>quadratique</mi><mo> </mo><mi>va</mi><mo> </mo><mi>changer</mi><mo> </mo><mi>pour</mi><mo> </mo><mi>constante</mi><mo> </mo><mi>avec</mi><mo> </mo><mo>"</mo><mi>a</mi><mo>"</mo></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Définition</mi><mo> </mo><mi>des</mi><mo> </mo><mi>fonctions</mi></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><msup><mi>x</mi><mn>2</mn></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><msup><mi>a</mi><mn>2</mn></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><mn>2</mn><mo>*</mo><mi>x</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Définition</mi><mo> </mo><mi>du</mi><mo> </mo><mi>plan</mi><mo> </mo><mi>de</mi><mo> </mo><mi>travail</mi><mo> </mo><mi>en</mi><mo> </mo><mi>tenant</mi><mo> </mo><mi>compte</mi><mo> </mo><mi>de</mi><mo> </mo><mi>a</mi><mo> </mo><mi>et</mi><mo> </mo><mi>de</mi><mo> </mo><msup><mi>a</mi><mrow><mn>2</mn><mo> </mo></mrow></msup><mi>pour</mi><mo> </mo><mi>les</mi><mo> </mo><mi>valeurs</mi><mo> </mo><mi>de</mi><mo> </mo><mo>"</mo><mi>y</mi><mo>"</mo></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tr</mi><mo>=</mo><mi>plotter</mi><mo>(</mo><mi>point</mi><mfenced><mrow><mn>0</mn><mo>,</mo><mn>0</mn></mrow></mfenced><mo>,</mo><mn>21</mn><mo>,</mo><mn>2</mn><msup><mi>a</mi><mn>2</mn></msup><mo>+</mo><mn>5</mn><mo>,</mo><mi>W</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>On</mi><mo> </mo><mi>trace</mi><mo> </mo><mi>les</mi><mo> </mo><mi>fonctions</mi><mo> </mo><mi>avec</mi><mo> </mo><mi>limite</mi><mo> </mo><mi>la</mi><mo> </mo><mi>valeur</mi><mo> </mo><mi>de</mi><mo> </mo><mo>"</mo><mi>a</mi><mo>"</mo></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>plot</mi><mo>(</mo><mi>f</mi><mo>,</mo><mn>0</mn><mo>.</mo><mo>.</mo><mi>a</mi><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>line_width</mi><mo>=</mo><mn>2</mn><mo>,</mo><mi>color</mi><mo>=</mo><mi>blue</mi></mtd></mtr></mtable></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>plot</mi><mo>(</mo><mi>g</mi><mo>,</mo><mi>a</mi><mo>.</mo><mo>.</mo><mi>a</mi><mo>+</mo><mn>4</mn><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>line_width</mi><mo>=</mo><mn>2</mn><mo>,</mo><mi>color</mi><mo>=</mo><mi>blue</mi></mtd></mtr></mtable></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>plot</mi><mo>(</mo><mi>h</mi><mo>,</mo><mn>0</mn><mo>.</mo><mo>.</mo><mo>-</mo><mi>a</mi><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>line_width</mi><mo>=</mo><mn>2</mn><mo>,</mo><mi>color</mi><mo>=</mo><mi>blue</mi></mtd></mtr></mtable></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Attribut</mi><mo> </mo><mi>graphique</mi><mo> </mo><mi>pour</mi><mo> </mo><mi>point</mi><mo> </mo><mi>ouvert</mi><mo> </mo><mi>en</mi><mo> </mo><mi>randomisant</mi><mo> </mo><mi>avec</mi><mo> </mo><mi>i</mi><mo> </mo><mi>et</mi><mo> </mo><mi>j</mi></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>j</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mo>=</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>j</mi><mo>=</mo><mn>2</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mrow><mi>PO1</mi><mo>=</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>point_size</mi><mo>=</mo><mn>6</mn><mo>,</mo><mi>color</mi><mo>=</mo><mi>red</mi></mtd></mtr></mtable></mfenced></mrow><mrow><mi>PO1</mi><mo>=</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>point_size</mi><mo>=</mo><mn>6</mn><mo>,</mo><mi>color</mi><mo>=</mo><mi>white</mi></mtd></mtr></mtable></mfenced></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>j</mi><mo>=</mo><mn>1</mn></mrow><mrow><mi>PO2</mi><mo>=</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>point_size</mi><mo>=</mo><mn>6</mn><mo>,</mo><mi>color</mi><mo>=</mo><mi>red</mi></mtd></mtr></mtable></mfenced></mrow><mrow><mi>PO2</mi><mo>=</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>point_size</mi><mo>=</mo><mn>6</mn><mo>,</mo><mi>color</mi><mo>=</mo><mi>white</mi></mtd></mtr></mtable></mfenced></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Bonne</mi><mo> </mo><mi>réponse</mi><mo> </mo><mi>en</mi><mo> </mo><mi>fonction</mi><mo> </mo><mi>de</mi><mo> </mo><mi>i</mi><mo> </mo><mi>et</mi><mo> </mo><mi>j</mi></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>i</mi><mo>=</mo><mn>1</mn><mo>∧</mo><mi>j</mi><mo>=</mo><mn>1</mn></mrow><mrow><mi>sol</mi><mo>=</mo><mo>[</mo><mo>-</mo><mi>a</mi><mo>,</mo><mi>a</mi><mo>+</mo><mn>4</mn><mo>]</mo></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>i</mi><mo>=</mo><mn>1</mn><mo>∧</mo><mi>j</mi><mo>=</mo><mn>2</mn></mrow><mrow><mi>sol</mi><mo>=</mo><mo>[</mo><mo>-</mo><mi>a</mi><mo>,</mo><mi>a</mi><mo>+</mo><mn>4</mn><mo>]</mo></mrow></apply></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>i</mi><mo>=</mo><mn>1</mn><mo>∧</mo><mi>j</mi><mo>=</mo><mn>1</mn></mrow><mrow><mi>sol</mi><mo>=</mo><mo>[</mo><mo>-</mo><mi>a</mi><mo>,</mo><mi>a</mi><mo>+</mo><mn>4</mn><mo>]</mo></mrow><mrow><mi>i</mi><mo>=</mo><mn>1</mn><mo>∧</mo><mi>j</mi><mo>=</mo><mn>2</mn></mrow><mtable><mtr><mtd><mi>sol</mi><mo>=</mo><mo>[</mo><mo>-</mo><mi>a</mi><mo>,</mo><mi>a</mi><mo>+</mo><mn>4</mn><mo>[</mo></mtd></mtr><mtr><mtd/></mtr></mtable><mrow/></apply></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>PO</mi><mo>=</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>point_size</mi><mo>=</mo><mn>6</mn><mo>,</mo><mi>color</mi><mo>=</mo><mi>white</mi></mtd></mtr></mtable></mfenced></math></comment></maction><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>PO</mi><mo>=</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd/></mtr></mtable></mfenced></math></comment></maction><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Astuce</mi><mo> </mo><mi>pour</mi><mo> </mo><mi>faire</mi><mo> </mo><mi>un</mi><mo> </mo><mi>point</mi><mo> </mo><mi>ouvert</mi></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>plot</mi><mo>(</mo><mi>point</mi><mo>(</mo><mo>-</mo><mi>a</mi><mo>,</mo><mi>h</mi><mo>(</mo><mo>-</mo><mi>a</mi><mo>)</mo><mo>)</mo><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>point_size</mi><mo>=</mo><mn>8</mn><mo>,</mo><mi>color</mi><mo>=</mo><mi>red</mi></mtd></mtr></mtable></mfenced><mo>)</mo></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>plot</mi><mo>(</mo><mi>point</mi><mo>(</mo><mo>-</mo><mi>a</mi><mo>,</mo><mi>h</mi><mo>(</mo><mo>-</mo><mi>a</mi><mo>)</mo><mo>)</mo><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>point_size</mi><mo>=</mo><mn>6</mn><mo>,</mo><mi>color</mi><mo>=</mo><mi>white</mi></mtd></mtr></mtable></mfenced><mo>)</mo></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>plot</mi><mo>(</mo><mi>point</mi><mo>(</mo><mo>-</mo><mi>a</mi><mo>,</mo><mi>h</mi><mo>(</mo><mo>-</mo><mi>a</mi><mo>)</mo><mo>)</mo><mo>,</mo><mi>PO1</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>plot</mi><mo>(</mo><mi>point</mi><mo>(</mo><mi>a</mi><mo>+</mo><mn>4</mn><mo>,</mo><msup><mi>a</mi><mn>2</mn></msup><mo>)</mo><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>point_size</mi><mo>=</mo><mn>8</mn><mo>,</mo><mi>color</mi><mo>=</mo><mi>red</mi></mtd></mtr></mtable></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>plot</mi><mo>(</mo><mi>point</mi><mo>(</mo><mi>a</mi><mo>+</mo><mn>4</mn><mo>,</mo><msup><mi>a</mi><mn>2</mn></msup><mo>)</mo><mo>,</mo><mi>PO2</mi><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="]" open="["><mrow><mo>-</mo><mn>6</mn><mo>,</mo><mn>10</mn></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">0.001</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data></localData></question> Domaine d'une fonction-suite de points Quel est le domaine de la fonction représentée ci-dessous ?

#plotter1

Domaine: {#1}{#2},{#3}{#4}

#plotter1

]]> 4.0000000 0.3333333 0 <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Paramétrage</mi><mo> </mo><mi>du</mi><mo> </mo><mi>plan</mi><mo> </mo><mi>cartésien</mi><mo> </mo><mi>utilisé</mi></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>WH</mi><mo>=</mo><mn>500</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>WW</mi><mo>=</mo><mn>500</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w1</mi><mo>:</mo><mo>=</mo><mi>show_axis</mi><mo>=</mo><mi>true</mi></math></input></command><command><input><math 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xmlns="http://www.w3.org/1998/Math/MathML"><mi>w7</mi><mo>:</mo><mo>=</mo><mi>grid_color</mi><mo>=</mo><mi>green</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w8</mi><mo>:</mo><mo>=</mo><mi>axis_style</mi><mo>=</mo><mo>"</mo><mi>arrow_xy</mi><mo>"</mo></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w9</mi><mo>:</mo><mo>=</mo><mi>axis_label</mi><mo>=</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>"</mo><mi>Le</mi><mo> </mo><mi>fonctionnement</mi><mo> </mo><mi>du</mi><mo> </mo><mi>moteur</mi><mo> </mo><mi>en</mi><mo> </mo><mi>secondes</mi><mo> </mo><mo> </mo><mo>"</mo><mo>,</mo><mo>"</mo><mi>L</mi><mo>'</mo><mi>altitude</mi><mo> </mo><mi>en</mi><mo> </mo><mi>mètres</mi><mo> </mo><mo> </mo><mo> </mo><mo>"</mo></mtd></mtr></mtable></mfenced></math></comment></maction><command><input><math 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</mo><mi>une</mi><mo> </mo><mi>fonction</mi><mo> </mo><mi>constante</mi><mo> </mo><mi>avec</mi><mo> </mo><mo>"</mo><mi>a</mi><mo>"</mo></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Définition</mi><mo> </mo><mi>des</mi><mo> </mo><mi>fonctions</mi></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><msup><mi>x</mi><mn>2</mn></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><msup><mi>a</mi><mn>2</mn></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><mn>2</mn><mo>*</mo><mi>x</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Définition</mi><mo> </mo><mi>du</mi><mo> </mo><mi>plan</mi><mo> </mo><mi>de</mi><mo> </mo><mi>travail</mi><mo> </mo><mi>en</mi><mo> </mo><mi>tenant</mi><mo> </mo><mi>compte</mi><mo> </mo><mi>de</mi><mo> </mo><mi>a</mi><mo> </mo><mi>et</mi><mo> </mo><mi>de</mi><mo> </mo><msup><mi>a</mi><mrow><mn>2</mn><mo> </mo></mrow></msup><mi>pour</mi><mo> </mo><mi>les</mi><mo> </mo><mi>valeurs</mi><mo> </mo><mi>de</mi><mo> </mo><mo>"</mo><mi>y</mi><mo>"</mo></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tr</mi><mo>=</mo><mi>plotter</mi><mo>(</mo><mi>point</mi><mfenced><mrow><mn>0</mn><mo>,</mo><mn>0</mn></mrow></mfenced><mo>,</mo><mn>21</mn><mo>,</mo><mn>2</mn><msup><mi>a</mi><mn>2</mn></msup><mo>+</mo><mn>5</mn><mo>,</mo><mi>W</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>On</mi><mo> </mo><mi>trace</mi><mo> </mo><mi>les</mi><mo> </mo><mi>fonctions</mi><mo> </mo><mi>avec</mi><mo> </mo><mi>limite</mi><mo> </mo><mi>la</mi><mo> </mo><mi>valeur</mi><mo> </mo><mi>de</mi><mo> </mo><mo>"</mo><mi>a</mi><mo>"</mo></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>plot</mi><mo>(</mo><mi>f</mi><mo>,</mo><mn>0</mn><mo>.</mo><mo>.</mo><mi>a</mi><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>line_width</mi><mo>=</mo><mn>2</mn><mo>,</mo><mi>color</mi><mo>=</mo><mi>blue</mi></mtd></mtr></mtable></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>plot</mi><mo>(</mo><mi>g</mi><mo>,</mo><mi>a</mi><mo>.</mo><mo>.</mo><mi>a</mi><mo>+</mo><mn>4</mn><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>line_width</mi><mo>=</mo><mn>2</mn><mo>,</mo><mi>color</mi><mo>=</mo><mi>blue</mi></mtd></mtr></mtable></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>plot</mi><mo>(</mo><mi>h</mi><mo>,</mo><mn>0</mn><mo>.</mo><mo>.</mo><mo>-</mo><mi>a</mi><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>line_width</mi><mo>=</mo><mn>2</mn><mo>,</mo><mi>color</mi><mo>=</mo><mi>blue</mi></mtd></mtr></mtable></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ai</mi><mo>=</mo><mi>h</mi><mo>(</mo><mo>-</mo><mi>a</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bi</mi><mo>=</mo><mi>f</mi><mo>(</mo><mi>a</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo>=</mo><mi>text_box</mi><mo>(</mo><mi>A</mi><mo>(</mo><mo>-</mo><mi>a</mi><mo>,</mo><mi>h</mi><mo>(</mo><mo>-</mo><mi>a</mi><mo>)</mo><mo>)</mo><mo>,</mo><mi>point</mi><mo>(</mo><mo>-</mo><mi>a</mi><mo>,</mo><mi>h</mi><mo>(</mo><mo>-</mo><mi>a</mi><mo>)</mo><mo>-</mo><mn>0</mn><mo>.</mo><mn>1</mn><mo>*</mo><msup><mi>a</mi><mn>2</mn></msup><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>a</mi><mo>=</mo><mn>6</mn></mrow><mrow><mi>k</mi><mo>=</mo><mn>2</mn><mo>.</mo><mn>5</mn></mrow><mrow><mi>k</mi><mo>=</mo><mn>3</mn></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi><mo>=</mo><mi>text_box</mi><mo>(</mo><mi>B</mi><mo>(</mo><mi>a</mi><mo>+</mo><mn>4</mn><mo>,</mo><mi>g</mi><mo>(</mo><mi>a</mi><mo>+</mo><mn>4</mn><mo>)</mo><mo>)</mo><mo>,</mo><mi>point</mi><mo>(</mo><mi>a</mi><mo>+</mo><mi>k</mi><mo>,</mo><mi>g</mi><mo>(</mo><mi>a</mi><mo>)</mo><mo>-</mo><mn>0</mn><mo>.</mo><mn>1</mn><mo>*</mo><msup><mi>a</mi><mn>2</mn></msup><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>plot</mi><mo>(</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>p1</mi><mo>,</mo><mi>p2</mi></mtd></mtr></mtable></mfenced><mo>)</mo></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Attribut</mi><mo> </mo><mi>graphique</mi><mo> </mo><mi>pour</mi><mo> </mo><mi>point</mi><mo> </mo><mi>ouvert</mi><mo> </mo><mi>en</mi><mo> </mo><mi>randomisant</mi><mo> </mo><mi>avec</mi><mo> </mo><mi>i</mi><mo> </mo><mi>et</mi><mo> </mo><mi>j</mi></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>j</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mrow><mi>PO1</mi><mo>=</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>point_size</mi><mo>=</mo><mn>6</mn><mo>,</mo><mi>color</mi><mo>=</mo><mi>red</mi></mtd></mtr></mtable></mfenced></mrow><mrow><mi>PO1</mi><mo>=</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>point_size</mi><mo>=</mo><mn>6</mn><mo>,</mo><mi>color</mi><mo>=</mo><mi>white</mi></mtd></mtr></mtable></mfenced></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>j</mi><mo>=</mo><mn>1</mn></mrow><mrow><mi>PO2</mi><mo>=</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>point_size</mi><mo>=</mo><mn>6</mn><mo>,</mo><mi>color</mi><mo>=</mo><mi>red</mi></mtd></mtr></mtable></mfenced></mrow><mrow><mi>PO2</mi><mo>=</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>point_size</mi><mo>=</mo><mn>6</mn><mo>,</mo><mi>color</mi><mo>=</mo><mi>white</mi></mtd></mtr></mtable></mfenced></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Bonne</mi><mo> </mo><mi>réponse</mi><mo> </mo><mi>en</mi><mo> </mo><mi>fonction</mi><mo> </mo><mi>de</mi><mo> </mo><mi>i</mi><mo> </mo><mi>et</mi><mo> </mo><mi>j</mi></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>i</mi><mo>=</mo><mn>1</mn><mo>∧</mo><mi>j</mi><mo>=</mo><mn>1</mn></mrow><mtable><mtr><mtd><mi>o1</mi><mo>=</mo><mo>"</mo><mo>[</mo><mo>"</mo></mtd></mtr><mtr><mtd><mi>a1</mi><mo>=</mo><mo>-</mo><mi>a</mi></mtd></mtr><mtr><mtd><mi>b</mi><mo>=</mo><mi>a</mi><mo>+</mo><mn>4</mn></mtd></mtr><mtr><mtd><mi>o2</mi><mo>=</mo><mo>"</mo><mo>]</mo><mo>"</mo></mtd></mtr></mtable><mrow><mi>i</mi><mo>=</mo><mn>1</mn><mo>∧</mo><mi>j</mi><mo>=</mo><mn>2</mn></mrow><mtable><mtr><mtd><mi>o1</mi><mo>=</mo><mo>"</mo><mo>[</mo><mo>"</mo></mtd></mtr><mtr><mtd><mi>a1</mi><mo>=</mo><mo>-</mo><mi>a</mi></mtd></mtr><mtr><mtd><mi>b</mi><mo>=</mo><mi>a</mi><mo>+</mo><mn>4</mn></mtd></mtr><mtr><mtd><mi>o2</mi><mo>=</mo><mo>"</mo><mo>[</mo><mo>"</mo></mtd></mtr></mtable><mrow><mi>i</mi><mo>=</mo><mn>2</mn><mo>∧</mo><mi>j</mi><mo>=</mo><mn>1</mn></mrow><mtable><mtr><mtd><mi>o1</mi><mo>=</mo><mo>"</mo><mo>]</mo><mo>"</mo></mtd></mtr><mtr><mtd><mi>a1</mi><mo>=</mo><mo>-</mo><mi>a</mi></mtd></mtr><mtr><mtd><mi>b</mi><mo>=</mo><mi>a</mi><mo>+</mo><mn>4</mn></mtd></mtr><mtr><mtd><mi>o2</mi><mo>=</mo><mo>"</mo><mo>]</mo><mo>"</mo></mtd></mtr></mtable><mtable><mtr><mtd><mi>o1</mi><mo>=</mo><mo>"</mo><mo>]</mo><mo>"</mo></mtd></mtr><mtr><mtd><mi>a1</mi><mo>=</mo><mo>-</mo><mi>a</mi></mtd></mtr><mtr><mtd><mi>b</mi><mo>=</mo><mi>a</mi><mo>+</mo><mn>4</mn></mtd></mtr><mtr><mtd><mi>o2</mi><mo>=</mo><mo>"</mo><mo>[</mo><mo>"</mo></mtd></mtr></mtable></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Astuce</mi><mo> </mo><mi>pour</mi><mo> </mo><mi>faire</mi><mo> </mo><mi>un</mi><mo> </mo><mi>point</mi><mo> </mo><mi>ouvert</mi></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>plot</mi><mo>(</mo><mi>point</mi><mo>(</mo><mo>-</mo><mi>a</mi><mo>,</mo><mi>h</mi><mo>(</mo><mo>-</mo><mi>a</mi><mo>)</mo><mo>)</mo><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>point_size</mi><mo>=</mo><mn>8</mn><mo>,</mo><mi>color</mi><mo>=</mo><mi>red</mi></mtd></mtr></mtable></mfenced><mo>)</mo></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>plot</mi><mo>(</mo><mi>point</mi><mo>(</mo><mo>-</mo><mi>a</mi><mo>,</mo><mi>h</mi><mo>(</mo><mo>-</mo><mi>a</mi><mo>)</mo><mo>)</mo><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>point_size</mi><mo>=</mo><mn>6</mn><mo>,</mo><mi>color</mi><mo>=</mo><mi>white</mi></mtd></mtr></mtable></mfenced><mo>)</mo></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>plot</mi><mo>(</mo><mi>point</mi><mo>(</mo><mo>-</mo><mi>a</mi><mo>,</mo><mi>h</mi><mo>(</mo><mo>-</mo><mi>a</mi><mo>)</mo><mo>)</mo><mo>,</mo><mi>PO1</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>plot</mi><mo>(</mo><mi>point</mi><mo>(</mo><mi>a</mi><mo>+</mo><mn>4</mn><mo>,</mo><msup><mi>a</mi><mn>2</mn></msup><mo>)</mo><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>point_size</mi><mo>=</mo><mn>8</mn><mo>,</mo><mi>color</mi><mo>=</mo><mi>red</mi></mtd></mtr></mtable></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>plot</mi><mo>(</mo><mi>point</mi><mo>(</mo><mi>a</mi><mo>+</mo><mn>4</mn><mo>,</mo><msup><mi>a</mi><mn>2</mn></msup><mo>)</mo><mo>,</mo><mi>PO2</mi><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>j</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>9</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>o1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><ms>]</ms></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>o2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><ms>]</ms></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ai</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>10</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bi</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>25</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">0.001</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data></localData></question> Fonction quadratique_image Quel choix de réponse correspond à l'image de la fonction:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»g«/mi»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«mo»=«/mo»«mo»#«/mo»«mi»a«/mi»«mo»§#183;«/mo»«msup»«mrow»«mo»(«/mo»«mi»x«/mi»«mo»-«/mo»«mo»#«/mo»«mi»h«/mi»«mo»)«/mo»«/mrow»«mn»2«/mn»«/msup»«mo»+«/mo»«mo»#«/mo»«mi»k«/mi»«/math»

]]> L'image d'une fonction quadratique de la forme: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»f«/mi»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«mo»=«/mo»«mi»a«/mi»«msup»«mrow»«mo»(«/mo»«mi»x«/mi»«mo»-«/mo»«mi»h«/mi»«mo»)«/mo»«/mrow»«mn»2«/mn»«/msup»«mo»+«/mo»«mi»k«/mi»«/math» dépend de deux paramètres:

le paramètre "a" qui donne l'ouverture de la parabole. Ici, #a est #signe, donc la parabole est ouverte vers le #ouv

le paramètre "k" qui donne la coordonnées en "y" du sommet de la parabole. Ici k = #k

La réponse est donc: #pr1#sol#pr2.

]]> 1.0000000 0.3333333 0 true true none Votre réponse est correcte. Votre réponse est partiellement correcte. Votre réponse est incorrecte. #pr1#sol#pr2

]]> #pr3#bad1#pr3

]]> #pr3#bad2#pr3

]]> #pr4#bad3#pr4

#plotter1