{"version":3,"file":"3F21-2-eTtAw_rl.js","sources":["../../src/exercices/3e/3F21-2.js"],"sourcesContent":["import { courbe } from '../../lib/2d/courbes.js'\nimport { point, tracePoint } from '../../lib/2d/points.js'\nimport { repere } from '../../lib/2d/reperes.js'\nimport { combinaisonListes } from '../../lib/outils/arrayOutils'\nimport { ecritureAlgebrique, ecritureParentheseSiNegatif } from '../../lib/outils/ecritures'\nimport Exercice from '../deprecatedExercice.js'\nimport { mathalea2d } from '../../modules/2dGeneralites.js'\nimport { listeQuestionsToContenu, randint } from '../../modules/outils.js'\nimport { fraction } from '../../modules/fractions.js'\nimport { ajouteChampTexteMathLive } from '../../lib/interactif/questionMathLive.js'\nimport { setReponse } from '../../lib/interactif/gestionInteractif.js'\n\nexport const titre = 'Determine an affine function using the images of two numbers'\nexport const interactifReady = true\nexport const interactifType = 'mathLive'\n\n/**\n * Déterminer la forme algébrique à partir de la donnée de 2 nombres et de leurs images\n * cas 0 : fonction constante\n * cas 1 : f(0) et f(x2) donnés\n * cas 2 : f(x1) et f(x1+1) donnés\n * cas 3 : f(x1) et f(x2) donnés a et b entiers\n * cas 4 : f(x1) et f(x2) donnés a et b rationnels\n * x1, x2, f(x1) et f(x2) sont toujours entiers relatifs\n * @author Jean-Claude Lhote\n * Référence 3F21-2\n */\nexport const uuid = 'b8b33'\nexport const ref = '3F21-2'\nexport default function DeterminerFonctionAffine () {\n  Exercice.call(this) // Héritage de la classe Exercice()\n  this.titre = titre\n  this.interactifReady = interactifReady\n  this.interactifType = interactifType\n  this.consigne = ''\n  this.sup = 1\n  this.nbQuestions = 2\n  this.nbCols = 2 // Uniquement pour la sortie LaTeX\n  this.nbColsCorr = 2 // Uniquement pour la sortie LaTeX\n  // this.sup = 1\n  this.tailleDiaporama = 3 // Pour les exercices chronométrés. 50 par défaut pour les exercices avec du texte\n  this.video = '' // Id YouTube ou url\n\n  this.nouvelleVersion = function () {\n    this.titre = titre\n\n    this.listeQuestions = [] // tableau contenant la liste des questions\n    this.listeCorrections = []\n    let typeDeQuestionsDisponibles\n    if (parseInt(this.sup) === 1) {\n      typeDeQuestionsDisponibles = [0, 1]\n    } else if (parseInt(this.sup) === 2) {\n      typeDeQuestionsDisponibles = [1, 2, 3]\n    } else {\n      typeDeQuestionsDisponibles = [3, 4]\n    }\n    const listeTypeDeQuestions = combinaisonListes(typeDeQuestionsDisponibles, this.nbQuestions)\n    for (let i = 0, x1, x2, y1, y2, a, b, tA, tB, r, texte, texteCorr, cpt = 0; i < this.nbQuestions && cpt < 50;) {\n      texte = '' // Nous utilisons souvent cette variable pour construire le texte de la question.\n      texteCorr = '' // Idem pour le texte de la correction.\n\n      switch (listeTypeDeQuestions[i]) {\n        case 0: // fonction constante\n          a = 0\n          b = randint(-10, 10, 0)\n          x1 = randint(-5, -1)\n          x2 = randint(1, 5)\n          y1 = b\n          y2 = b\n          texteCorr = `We notice that $f(${x1})=f(${x2})=${b}$ therefore the line representing the function $f$ passes through two distinct points having the same ordinate.<br>`\n          texteCorr += `It is therefore parallel to the abscissa axis. The function $f$ is a constant function and $f(x)=${b}$.`\n          setReponse(this, i, `f(x)=${b}`)\n          if (this.correctionDetaillee) {\n            tA = tracePoint(point(x1, y1), 'red')\n            tB = tracePoint(point(x2, y2), 'red')\n\n            r = repere({ xMin: -5, yMin: Math.min(-1, b - 1), xMax: 5, yMax: Math.max(b + 1, 2) })\n            texteCorr += `<br><br>${mathalea2d({ xmin: -5, ymin: Math.min(-1, b - 1), xmax: 5, ymax: Math.max(b + 1, 2), pixelsParCm: 20, scale: 0.7 }, r, courbe(x => a * x + b, { mark: r, color: 'blue' }), tA, tB)}`\n          }\n          break\n\n        case 1: // f(0)=y1 f(x2)= y2 a et b entiers relatifs.\n          a = randint(-2, 2, 0)\n          b = randint(-5, 5, 0)\n          x1 = 0\n          y1 = b\n          x2 = randint(-5, 5, 0)\n          y2 = b + a * x2\n          texteCorr = `Let $f(x)=ax+b$. We know that $f(0)=${y1}=b$.<br>`\n          texteCorr += `So $f(x)=ax${ecritureAlgebrique(y1)}$. Using the data $f(${x2})=${y2}$ we obtain: $a \\\\times ${ecritureParentheseSiNegatif(x2)}${ecritureAlgebrique(b)} = ${y2}$ hence $a \\\\times ${ecritureParentheseSiNegatif(x2)} = ${y2}${ecritureAlgebrique(-b)} = ${y2 - b}$ therefore $a=\\\\dfrac{${y2 - b}}{${x2} } = ${a}$.<br>`\n          texteCorr += `So $f(x)=${a}x${ecritureAlgebrique(b)}$.`\n          setReponse(this, i, `f(x)=${a}x${ecritureAlgebrique(b)}`)\n          if (this.correctionDetaillee) {\n            tA = tracePoint(point(x1, y1), 'red')\n            tB = tracePoint(point(x2, y2), 'red')\n\n            r = repere({\n              xMin: -5,\n              yMin: Math.min(-5 * a + b, 5 * a + b),\n              xMax: 5,\n              yMax: Math.max(-5 * a + b, 5 * a + b)\n            })\n            texteCorr += `<br><br>${mathalea2d({ xmin: -5, ymin: Math.min(-5 * a + b, 5 * a + b), xmax: 5, ymax: Math.max(-5 * a + b, 5 * a + b), pixelsParCm: 20, scale: 0.7 }, r, courbe(x => a * x + b, { mark: r, color: 'blue' }), tA, tB)}`\n          }\n          break\n\n        case 2: // f(x1)=y1 et f(x1+1)=y2\n          a = randint(-5, 5, 0)\n          b = randint(-5, 5, 0)\n          x1 = randint(-5, 5, [-1, 0])\n          y1 = a * x1 + b\n          x2 = x1 + 1\n          y2 = b + a * x2\n          texteCorr = `Let $f(x)=ax+b$. We go from $${x1}$ to $${x2}$ by adding 1, so the slope $a$ of the line corresponds to $f(${x2})-f(${x1})=${y2}-${ecritureParentheseSiNegatif(y1)}=`\n          if (y1 < 0) texteCorr += `${y2}${ecritureAlgebrique(-y1)} = ${a}$.<br>`\n          else texteCorr += `${a}$.<br>`\n          texteCorr += `So $f(x)=${a}x+b$.<br>Using the data $f(${x2})=${y2}$ we obtain: $${a} \\\\times ${ecritureParentheseSiNegatif(x2)}+b=${y2}$ hence $${a * x2}+b=${y2} $ therefore $b=${y2}${ecritureAlgebrique(-a * x2)} = ${b}$.<br>`\n          texteCorr += `So $f(x)=${a}x${ecritureAlgebrique(b)}$.`\n          setReponse(this, i, `f(x)=${a}x${ecritureAlgebrique(b)}`)\n          if (this.correctionDetaillee) {\n            tA = tracePoint(point(x1, y1), 'red')\n            tB = tracePoint(point(x2, y2), 'red')\n\n            r = repere({\n              xMin: -5,\n              yMin: Math.min(-5 * a + b, 5 * a + b),\n              xMax: 5,\n              yMax: Math.max(-5 * a + b, 5 * a + b)\n            })\n            texteCorr += `<br><br>${mathalea2d({ xmin: -5, ymin: Math.min(-5 * a + b, 5 * a + b), xmax: 5, ymax: Math.max(-5 * a + b, 5 * a + b), pixelsParCm: 20, scale: 0.7 }, r, courbe(x => a * x + b, { mark: r, color: 'blue' }), tA, tB)}`\n          }\n          break\n\n        case 3: // f(x1)=y1 f(x2)=y2 a et b entiers\n          a = randint(-5, 5, 0)\n          b = randint(-5, 5, 0)\n          x1 = randint(-5, 5, 0)\n          y1 = a * x1 + b\n          x2 = randint(-5, 5, [0, x1])\n          y2 = b + a * x2\n          texteCorr = `Let $f(x)=ax+b$. Using the data from the statement, we obtain: $f(${x1})=${y1}=a \\\\times ${ecritureParentheseSiNegatif(x1)}+b$ and $f(${x2})=${y2}=a \\\\times ${ecritureParentheseSiNegatif(x2)}+b$<br>`\n          texteCorr += `So on the one hand: $b=${y1}+a\\\\times ${ecritureParentheseSiNegatif(-x1)}$ and on the other hand: $b=${y2}+a\\\\times ${ecritureParentheseSiNegatif(-x2)}$.<br>`\n          texteCorr += `By identification, we obtain: $${y1}+a\\\\times ${ecritureParentheseSiNegatif(-x1)} = ${y2}+a\\\\times ${ecritureParentheseSiNegatif(-x2)}$.<br>`\n          texteCorr += `We deduce that $${y1}${ecritureAlgebrique(-y2)}=a(${x1}${ecritureAlgebrique(-x2)})$ is $${y1 - y2} = ${x1 - x2}a$.<br>`\n          texteCorr += `So $a=\\\\dfrac{${y1 - y2}}{${x1 - x2}} = ${a}$.<br>`\n          texteCorr += `So $b=${y1}${ecritureAlgebrique(a)}\\\\times ${ecritureParentheseSiNegatif(-x1)} = ${y1}${ecritureAlgebrique(-a * x1)} = ${b}$.<br>`\n          texteCorr += `So $f(x)=${a}x${ecritureAlgebrique(b)}$.`\n          setReponse(this, i, `f(x)=${a}x${ecritureAlgebrique(b)}`)\n          if (this.correctionDetaillee) {\n            tA = tracePoint(point(x1, y1), 'red')\n            tB = tracePoint(point(x2, y2), 'red')\n\n            r = repere({\n              xMin: -5,\n              yMin: Math.min(-5 * a + b, 5 * a + b),\n              xMax: 5,\n              yMax: Math.max(-5 * a + b, 5 * a + b)\n            })\n            texteCorr += `<br><br>${mathalea2d({ xmin: -5, ymin: Math.min(-5 * a + b, 5 * a + b), xmax: 5, ymax: Math.max(-5 * a + b, 5 * a + b), pixelsParCm: 20, scale: 0.7 }, r, courbe(x => a * x + b, { mark: r, color: 'blue' }), tA, tB)}`\n          }\n          break\n\n        case 4:\n          x1 = randint(-5, 5, 0)\n          x2 = randint(-5, 5, [0, x1])\n          y1 = randint(-5, 5)\n          y2 = randint(-5, 5)\n          a = fraction(y2 - y1, x2 - x1)\n          b = a.multiplieEntier(-x1).ajouteEntier(y1)\n          texteCorr = `Let $f(x)=ax+b$. Using the data from the statement, we obtain: $f(${x1})=${y1}=a \\\\times ${ecritureParentheseSiNegatif(x1)}+b$ and $f(${x2})=${y2}=a \\\\times ${ecritureParentheseSiNegatif(x2)}+b$<br>`\n          texteCorr += `So on the one hand: $b=${y1}+a\\\\times ${ecritureParentheseSiNegatif(-x1)}$ and on the other hand: $b=${y2}+a\\\\times ${ecritureParentheseSiNegatif(-x2)}$.<br>`\n          texteCorr += `By identification, we obtain: $${y1}+a\\\\times ${ecritureParentheseSiNegatif(-x1)} = ${y2}+a\\\\times ${ecritureParentheseSiNegatif(-x2)}$.<br>`\n          texteCorr += `We deduce that $${y1}${ecritureAlgebrique(-y2)}=a(${x1}${ecritureAlgebrique(-x2)})$ is $${y1 - y2} = ${x1 - x2}a$.<br>`\n          texteCorr += `So $a=\\\\dfrac{${y1 - y2}}{${x1 - x2}} = ${a.texFractionSimplifiee}$.<br>`\n          texteCorr += `So $b=${y1}+${a.texFractionSimplifiee}\\\\times ${ecritureParentheseSiNegatif(-x1)} = ${fraction(y1 * a.denIrred, a.denIrred).texFraction}+${a.multiplieEntier(-x1).texFractionSimplifiee} = ${b.texFractionSimplifiee}$.<br>`\n          texteCorr += `So $f(x)=${a.texFractionSimplifiee}x${b.simplifie().texFractionSignee}$.`\n          setReponse(this, i, `f(x)=${a.texFractionSimplifiee}x${b.simplifie().texFractionSignee}`)\n          if (this.correctionDetaillee) {\n            tA = tracePoint(point(x1, y1), 'red')\n            tB = tracePoint(point(x2, y2), 'red')\n\n            a = a.n / a.d\n            b = b.n / b.d\n            r = repere({\n              xMin: -5,\n              yMin: Math.round(Math.min(-5 * a + b, 5 * a + b)),\n              xMax: 5,\n              yMax: Math.round(Math.max(-5 * a + b, 5 * a + b))\n            })\n            texteCorr += `<br><br>${mathalea2d({ xmin: -5, ymin: Math.round(Math.min(-5 * a + b, 5 * a + b)), xmax: 5, ymax: Math.round(Math.max(-5 * a + b, 5 * a + b)), pixelsParCm: 20, scale: 0.7 }, r, courbe(x => a * x + b, { mark: r, color: 'blue' }), tA, tB)}`\n          }\n          break\n      }\n      texte = `The function $f$ is an affine function and we know that $f(${x1})=${y1}$ and $f(${x2})=${y2}$.<br>`\n      texte += 'Determine the algebraic form of the function $f$.'\n      texte += ajouteChampTexteMathLive(this, i)\n      if (this.questionJamaisPosee(i, x1, x2, y1, y2, a, b, listeTypeDeQuestions[i])) {\n        // If the question has never been asked, we store it in the list of questions\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  }\n  this.besoinFormulaireNumerique = ['Difficulty level', 3, '1: Easy\\n2: Difficult\\n3: Very 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