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{"version":3,"file":"2F31-3-y2Rw2Fy2.js","sources":["../../src/exercices/2e/2F31-3.js"],"sourcesContent":["import { propositionsQcm } from '../../lib/interactif/qcm.js'\nimport { tableauDeVariation } from '../../lib/mathFonctions/etudeFonction.js'\nimport { choice, combinaisonListes } from '../../lib/outils/arrayOutils'\nimport { context } from '../../modules/context.js'\nimport { listeQuestionsToContenu, randint } from '../../modules/outils.js'\nimport Exercice from '../deprecatedExercice.js'\n\nexport const titre = 'Compare images in a variation table'\nexport const interactifReady = true\nexport const interactifType = 'qcm'\n// Les exports suivants sont optionnels mais au moins la date de publication semble essentielle\nexport const dateDePublication = '25/10/2021' // La date de publication initiale au format 'jj/mm/aaaa' pour affichage temporaire d'un tag\nexport const dateDeModifImportante = '17/05/2023' // Une date de modification importante au format 'jj/mm/aaaa' pour affichage temporaire d'un tag\n/**\n * Description didactique de l'exercice\n * @author Stéphane Guyon modif Gilles Mora\n * Référence 2F31-3\n */\nexport const uuid = 'c705b'\nexport const ref = '2F31-3'\nexport default function Variationsapartirtableau () {\n Exercice.call(this) // Héritage de la classe Exercice()\n this.nbQuestions = 1 // Nombre de questions par défaut\n this.video = '' // Id YouTube ou url\n this.listePackages = ['tkz-tab']//, 'tkz-fct', 'tkz-euclide'\n\n this.nouvelleVersion = function () {\n this.listeQuestions = [] // Liste de questions\n this.listeCorrections = [] // Liste de questions corrigées\n\n const typeQuestionsDisponibles = ['type1', 'type2', 'type3', 'type4', 'type5']//\n this.nbQuestionsModifiable = true\n const listeTypeQuestions = combinaisonListes(typeQuestionsDisponibles, this.nbQuestions) // Tous les types de questions sont posés mais l'ordre diffère à chaque 'cycle'\n for (let i = 0, ligne1, a1, a2, a3, a4, x1, x2, x3, y1, y2, y3, texte, texteCorr, cpt = 0; i < this.nbQuestions && cpt < 50;) { // Boucle principale où i+1 correspond au numéro de la question\n texte = 'We give below the table of variations of a function $f$.'\n texte += ' <br>'\n x1 = randint(-8, -3) // 3 antécédents 1ère ligne tableau\n x2 = randint(x1 + 10, x1 + 17)// 3 antécédents 1ère ligne tableau\n x3 = randint(x2 + 6, x2 + 15)// 3 antécédents 1ère ligne tableau\n y1 = randint(-12, -2)// 3 images des antécédents 1ère ligne tableau\n y2 = randint(y1 + 2, y1 + 10)// 3 images des antécédents 1ère ligne tableau\n y3 = randint(y1 + 2, y2 - 2, [y2])// 3 images des antécédents 1ère ligne tableau\n a1 = randint(x1 + 1, x1 + 4) // 1er antécédent dont on doit comparer l'image\n a2 = randint(a1 + 1, x2 - 1) // 2eme antécédent dont on doit comparer l'image\n a3 = randint(x2 + 1, x3 - 6) // 3eme antécédent dont on doit comparer l'image\n a4 = randint(a3 + 1, x3 - 1) // 4eme antécédent dont on doit comparer l'image\n switch (listeTypeQuestions[i]) { // Suivant le type de question, le contenu sera différent\n case 'type1':// parabole en U ; 2 images sur intervalle où f croissant\n texte += `From the information in the statement, compare if possible: $f(${a1})$ and $f(${a2})$.<br><br>`\n ligne1 = ['Var', 10, `-/$${y1}$`, 10, `+/$${y2}$`, 10, `-/$${y3}$`, 10] // Commencer chaque chaîne par +/ ou -/ pour indiquer le sens de la variation, 'R/' pour 'skip a box'\n\n // xmin determines the margin on the left, ymin the height reserved for the table, xmax the width reserved for the table and ymax the margin above the table\n texte += tableauDeVariation({\n tabInit: [\n [\n // First column of the table with the format [header string, line height, number of pixels of estimated text width for centering]\n ['$x$', 2, 10], ['$f(x)$', 4, 30]\n ],\n // First row of the table with each antecedent followed by its number of pixels of estimated text width for centering\n [`$${x1}$`, 10, `$${x2}$`, 10, `$${x3}$`, 10]\n ],\n // tabLines below contains the other rows of the table.\n tabLines: [ligne1],\n colorBackground: '',\n espcl: 2, // taille en cm entre deux antécédents\n deltacl: 0.8, // distance entre la bordure et les premiers et derniers antécédents\n lgt: 3 // taille de la première colonne en cm\n })\n texteCorr = `According to the variation table, the function $f$ is increasing on $[${x1},${x2}]$. <br>`\n texteCorr += `Additionally, $${a1}\\\\in[${x1},${x2}]$, $${a2}\\\\in[${x1},${x2}]$ and $${a1}<${a2}$.<br>`\n if (context.isHtml) {\n ligne1 = ['Var', 5, `-/$${y1}$`, 5, 't/', 5, 't/', 5, `+/$${y2}$`, 5, `-/$${y3}$`, 5]\n // xmin determines the margin on the left, ymin the height reserved for the table, xmax the width reserved for the table and ymax the margin above the table\n texteCorr += tableauDeVariation({\n tabInit: [\n [\n // First column of the table with the format [header string, line height, number of pixels of estimated text width for centering]\n ['$x$', 2, 10], ['$f(x)$', 4, 10]\n ],\n // First row of the table with each antecedent followed by its number of pixels of estimated text width for centering\n [`$${x1}$`, 5, `$${a1}$`, 5, `$${a2}$`, 5, `$${x2}$`, 5, `$${x3}$`, 5]\n // ['Val', 1, 2, 0.3, `$${x1}$`, `$f(${x1})$`, 0.5]\n ],\n // long=0.5\n // tabLines below contains the other rows of the table.\n tabLines: [ligne1],\n colorBackground: '',\n espcl: 3, // taille en cm entre deux antécédents\n deltacl: 0.8, // distance entre la bordure et les premiers et derniers antécédents\n lgt: 3 // taille de la première colonne en cm\n })\n } else {\n texteCorr += `<br>\\\\begin{tikzpicture}%[scale=0.6]\\\\tkzTabInit[lgt=1.5,espcl=5]{$x$/1,$f(x)$/2}{$${x1}$,$${x2} $,$${x3}$}\\\\tkzTabVar{-/$${y1}$,+/$${y2}$,-/$${y3}$}\\\\tkzTabVal[draw]{1}{2}{0.3}{$${a1}$}{$ f(${a1})$}\\\\tkzTabVal[draw]{1}{2}{0.6}{$${a2}$}{$f(${a2})$}\\\\end{tikzpicture}<br><br>`\n }\n if (this.interactif) {\n this.autoCorrection[i] = {\n enonce: texte,\n options: { horizontal: true },\n propositions: [\n {\n texte: `${choice([true, false]) ? `$f(${a2}) > f(${a1})$` : `$f(${a1}) < f(${a2})$`}`,\n statut: true\n },\n {\n texte: `${choice([true, false]) ? `$f(${a1}) > f(${a2})$` : `$f(${a2}) < f(${a1})$`}`,\n statut: false\n },\n {\n texte: 'We can not know',\n statut: false\n }\n ]\n }\n texte += propositionsQcm(this, i).texte\n }\n texteCorr += 'We know that if a function is increasing on an interval $[a,b]$, '\n texteCorr += 'then its antecedents and its images are arranged in the same order.<br>'\n texteCorr += 'This means that for all $x_1\\\\in[a,b]$ and $x_2\\\\in[a,b]$, '\n texteCorr += 'if $x_1 < x_2$ then $f(x_1) < f(x_2)$. <br><br>'\n texteCorr += `Therefore, since $${a1}<${a2}$, then $f(${a1}) < f(${a2})$. `\n break\n case 'type2':// parabole en U ; 2 images sur intervalle où f décroissant\n texte += `From the information in the statement, compare if possible: $f(${a3})$ and $f(${a4})$.<br>`\n ligne1 = ['Var', 10, `-/$${y1}$`, 10, `+/$${y2}$`, 10, `-/$${y3}$`, 10] // Commencer chaque chaîne par +/ ou -/ pour indiquer le sens de la variation, 'R/' pour 'skip a box'\n\n // xmin determines the margin on the left, ymin the height reserved for the table, xmax the width reserved for the table and ymax the margin above the table\n texte += tableauDeVariation({\n tabInit: [\n [\n // First column of the table with the format [header string, line height, number of pixels of estimated text width for centering]\n ['$x$', 2, 10], ['$f(x)$', 4, 30]\n ],\n // First row of the table with each antecedent followed by its number of pixels of estimated text width for centering\n [`$${x1}$`, 10, `$${x2}$`, 10, `$${x3}$`, 10]\n ],\n // tabLines below contains the other rows of the table.\n tabLines: [ligne1],\n colorBackground: '',\n espcl: 2, // taille en cm entre deux antécédents\n deltacl: 0.8, // distance entre la bordure et les premiers et derniers antécédents\n lgt: 3 // taille de la première colonne en cm\n })\n\n texteCorr = `According to the variation table, the function $f$ is decreasing on $[${x2},${x3}]$.<br>Furthermore, `\n texteCorr += ` $${a3}\\\\in[${x2},${x3}]$, $${a4}\\\\in[${x2},${x3}]$ and $${a3}<${a4}$.<br>`\n if (context.isHtml) {\n ligne1 = ['Var', 5, `-/$${y1}$`, 5, `+/$${y2}$`, 5, 't/', 5, 't/', 5, `-/$${y3}$`, 5] // Commencer chaque chaîne par +/ ou -/ pour indiquer le sens de la variation, 'R/' pour 'skip a box'\n texteCorr += tableauDeVariation({\n tabInit: [\n [\n // First column of the table with the format [header string, line height, number of pixels of estimated text width for centering]\n ['$x$', 2, 10], ['$f(x)$', 3, 50]\n ],\n // First row of the table with each antecedent followed by its number of pixels of estimated text width for centering\n [`$${x1}$`, 5, `$${x2}$`, 5, `$${a3}$`, 5, `$${a4}$`, 5, `$${x3}$`, 5]\n ],\n // tabLines below contains the other rows of the table.\n tabLines: [ligne1],\n colorBackground: '',\n espcl: 3.5, // taille en cm entre deux antécédents\n deltacl: 0.8, // distance entre la bordure et les premiers et derniers antécédents\n lgt: 3 // taille de la première colonne en cm\n })\n } else {\n texteCorr += `<br>\\\\begin{tikzpicture}%[scale=0.6]\\\\tkzTabInit[lgt=1.5,espcl=5]{$x$/1,$f(x)$/2}{$${x1}$,$${x2} $,$${x3}$}\\\\tkzTabVar{-/$${y1}$,+/$${y2}$,-/$${y3}$}\\\\tkzTabVal[draw]{2}{3}{0.3}{$${a3}$}{$ f(${a3})$}\\\\tkzTabVal[draw]{2}{3}{0.6}{$${a4}$}{$f(${a4})$}\\\\end{tikzpicture}<br><br>`\n }\n if (this.interactif) {\n this.autoCorrection[i] = {\n enonce: texte,\n options: { horizontal: true },\n propositions: [\n {\n texte: `${choice([true, false]) ? `$f(${a3}) > f(${a4})$` : `$f(${a4}) < f(${a3})$`}`,\n statut: true\n },\n {\n texte: `${choice([true, false]) ? `$f(${a3}) < f(${a4})$` : `$f(${a4}) > f(${a3})$`}`,\n statut: false\n },\n {\n texte: 'We can not know',\n statut: false\n }\n ]\n }\n texte += propositionsQcm(this, i).texte\n }\n texteCorr += 'We know that if a function is decreasing on an interval $[a,b]$, '\n texteCorr += 'then its antecedents and images are arranged in reverse order. <br>'\n texteCorr += 'This means that for all $x_1\\\\in[a,b]$ and $x_2\\\\in[a,b]$, '\n texteCorr += 'if $x_1 < x_2$ then $f(x_1) > f(x_2)$. <br><br>'\n texteCorr += `Therefore, since $${a3}<${a4}$, then $f(${a3}) > f(${a4})$. `\n break\n case 'type3':// parabole en U ; 2 images sur intervalle où f pas monotone, mais on peut répondre\n texte += `From the information in the statement, compare if possible: $f(${a1})$ and $f(${x3})$.<br>`\n y3 = randint(y1 - 12, y1 - 2)// 3 images des antécédents 1ère ligne tableau\n ligne1 = ['Var', 10, `-/$${y1}$`, 30, `+/$${y2}$`, 30, `-/$${y3}$`, 30] // Commencer chaque chaîne par +/ ou -/ pour indiquer le sens de la variation, 'R/' pour 'skip a box'\n\n // xmin determines the margin on the left, ymin the height reserved for the table, xmax the width reserved for the table and ymax the margin above the table\n texte += tableauDeVariation({\n tabInit: [\n [\n // First column of the table with the format [header string, line height, number of pixels of estimated text width for centering]\n ['$x$', 2, 10], ['$f(x)$', 4, 30]\n ],\n // First row of the table with each antecedent followed by its number of pixels of estimated text width for centering\n [`$${x1}$`, 10, `$${x2}$`, 10, `$${x3}$`, 10]\n ],\n // tabLines below contains the other rows of the table.\n tabLines: [ligne1],\n colorBackground: '',\n espcl: 3.5, // taille en cm entre deux antécédents\n deltacl: 0.8, // distance entre la bordure et les premiers et derniers antécédents\n lgt: 3 // taille de la première colonne en cm\n })\n\n texteCorr = `According to the variation table, $f(${x3})=${y3}$.<br>`\n texteCorr += `On the other hand, $${a1}\\\\in[${x1},${x2}]$, interval on which the function $f$ is increasing.<br>`\n texteCorr += 'We know that if a function is increasing on an interval $[a,b]$, '\n texteCorr += 'then its antecedents and its images are arranged in the same order.<br>'\n texteCorr += 'This means that for all $x_1\\\\in[a,b]$ and $x_2\\\\in[a,b]$, '\n texteCorr += 'if $x_1 < x_2$ then $f(x_1) < f(x_2)$. <br>'\n texteCorr += `Therefore, since $${x1}<${a1}$, then $f(${x1}) < f(${a1})$. `\n texteCorr += `<br>As $f(${x1}) =${y1}$, we showed that: $f(${a1}) > ${y1}$.<br><br>`\n texteCorr += `We deduce that: $f(${a1}) > ${y1} > ${y3} > f(${x3})$.<br>`\n if (this.interactif) {\n this.autoCorrection[i] = {\n enonce: texte,\n options: { horizontal: true },\n propositions: [\n {\n texte: `${choice([true, false]) ? `$f(${a1}) > f(${x3})$` : `$f(${x3}) < f(${a1})$`}`,\n statut: true\n },\n {\n texte: `${choice([true, false]) ? `$f(${a1}) < f(${x3})$` : `$f(${x3}) > f(${a1})$`}`,\n statut: false\n },\n {\n texte: 'We can not know',\n statut: false\n }\n ]\n }\n texte += propositionsQcm(this, i).texte\n }\n break\n case 'type4':// parabole en U ; 2 images sur intervalle où f pas monotone, et on ne peut pas répondre\n texte += `From the information in the statement, compare if possible: $f(${a1})$ and $f(${x3})$.<br>`\n y3 = randint(y1 + 2, y2 - 1)// 3 images des antécédents 1ère ligne tableau\n ligne1 = ['Var', 10, `-/$${y1}$`, 10, `+/$${y2}$`, 10, `-/$${y3}$`, 10] // Commencer chaque chaîne par +/ ou -/ pour indiquer le sens de la variation, 'R/' pour 'skip a box'\n\n // xmin determines the margin on the left, ymin the height reserved for the table, xmax the width reserved for the table and ymax the margin above the table\n texte += tableauDeVariation({\n tabInit: [\n [\n // First column of the table with the format [header string, line height, number of pixels of estimated text width for centering]\n ['$x$', 2, 10], ['$f(x)$', 3, 30]\n ],\n // First row of the table with each antecedent followed by its number of pixels of estimated text width for centering\n [`$${x1}$`, 10, `$${x2}$`, 10, `$${x3}$`, 10]\n ],\n // tabLines below contains the other rows of the table.\n tabLines: [ligne1],\n colorBackground: '',\n espcl: 3.5, // taille en cm entre deux antécédents\n deltacl: 0.8, // distance entre la bordure et les premiers et derniers antécédents\n lgt: 3 // taille de la première colonne en cm\n })\n\n texteCorr = `According to the variation table, $f(${x3})=${y3}$.<br>`\n texteCorr += `On the other hand, $${a1}\\\\in[${x1},${x2}]$, interval on which the function $f$ is increasing.<br>`\n texteCorr += 'We know that if a function is increasing on an interval $[a,b]$, '\n texteCorr += 'then its antecedents and its images are arranged in the same order.<br>'\n texteCorr += 'This means that for all $x_1\\\\in[a,b]$ and $x_2\\\\in[a,b]$, '\n texteCorr += 'if $x_1 < x_2$ then $f(x_1) < f(x_2)$. <br>'\n texteCorr += `Therefore, since $${x1}<${a1}<${x2}$, then $f(${x1})< f(${a1}) < f(${x2})$. `\n texteCorr += `<br>We have therefore shown that: $${y1} < f(${a1}) < ${y2}$.<br><br>`\n texteCorr += `As $f(${x3})=${y3} \\\\in [${y1},${y2}]$, `\n texteCorr += `we cannot conclude without more information to compare $f(${x3})$ and $f(${a1})$. `\n if (this.interactif) {\n this.autoCorrection[i] = {\n enonce: texte,\n options: { horizontal: true },\n propositions: [\n {\n texte: `${choice([true, false]) ? `$f(${x3}) > f(${a1})$` : `$f(${a1}) < f(${x3})$`}`,\n statut: false\n },\n {\n texte: `${choice([true, false]) ? `$f(${x3}) < f(${a1})$` : `$f(${a1}) > f(${x3})$`}`,\n statut: false\n },\n {\n texte: 'We can not know',\n statut: true\n }\n ]\n }\n texte += propositionsQcm(this, i).texte\n }\n break\n case 'type5':// parabole en U ; 2 images sur intervalle où f non monotone. On ne peut conclure\n texte += `From the information in the statement, compare if possible: $f(${a1})$ and $f(${a3})$.<br>`\n ligne1 = ['Var', 10, `-/$${y1}$`, 10, `+/$${y2}$`, 10, `-/$${y3}$`, 10] // Commencer chaque chaîne par +/ ou -/ pour indiquer le sens de la variation, 'R/' pour 'skip a box'\n\n // xmin determines the margin on the left, ymin the height reserved for the table, xmax the width reserved for the table and ymax the margin above the table\n texte += tableauDeVariation({\n tabInit: [\n [\n // First column of the table with the format [header string, line height, number of pixels of estimated text width for centering]\n ['$x$', 2, 10], ['$f(x)$', 4, 30]\n ],\n // First row of the table with each antecedent followed by its number of pixels of estimated text width for centering\n [`$${x1}$`, 10, `$${x2}$`, 10, `$${x3}$`, 10]\n ],\n // tabLines below contains the other rows of the table.\n tabLines: [ligne1],\n colorBackground: '',\n espcl: 3.5, // taille en cm entre deux antécédents\n deltacl: 0.8, // distance entre la bordure et les premiers et derniers antécédents\n lgt: 3 // taille de la première colonne en cm\n })\n\n texteCorr = `According to the variation table:<br>$\\\\bullet$ $${a1}\\\\in[${x1},${x2}]$, interval over which the function is increasing. `\n texteCorr += ` <br>$\\\\bullet$ $${a3}\\\\in[${x2},${x3}]$, interval over which the function is decreasing. <br><br>`\n texteCorr += `The function $f$ is therefore not monotonic on $[${a1},${a3}]$.<br><br>`\n texteCorr += ` The variation table does not allow $f(${a1})$ and $f(${a3})$ to be compared. <br>`\n texteCorr += 'We cannot therefore conclude without more information.'\n if (this.interactif) {\n this.autoCorrection[i] = {\n enonce: texte,\n options: { horizontal: true },\n propositions: [\n {\n texte: `${choice([true, false]) ? `$f(${a3}) > f(${a1})$` : `$f(${a1}) < f(${a3})$`}`,\n statut: false\n },\n {\n texte: `${choice([true, false]) ? `$f(${a3}) < f(${a1})$` : `$f(${a1}) > f(${a3})$`}`,\n statut: false\n },\n {\n texte: 'We can not know',\n statut: true\n }\n ]\n }\n texte += propositionsQcm(this, i).texte\n }\n break\n }\n // If the question has never been asked, we save it\n if (this.questionJamaisPosee(i, texte)) { // <- laisser le i et ajouter toutes les variables qui rendent les exercices différents (par exemple a, b, c et d)\n this.listeQuestions.push(texte)\n this.listeCorrections.push(texteCorr)\n i++\n }\n cpt++\n }\n listeQuestionsToContenu(this) // On envoie l'exercice à la fonction de mise en page\n 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