{"version":3,"file":"2F10-3-tSkPJRMp.js","sources":["../../src/exercices/2e/2F10-3.js"],"sourcesContent":["import { droite } from '../../lib/2d/droites.js'\nimport { point, tracePoint } from '../../lib/2d/points.js'\nimport { repere } from '../../lib/2d/reperes.js'\nimport { labelPoint, texteParPosition } from '../../lib/2d/textes.js'\nimport { choice, combinaisonListes } from '../../lib/outils/arrayOutils'\nimport { texFractionReduite } from '../../lib/outils/deprecatedFractions.js'\nimport { ecritureAlgebrique, ecritureParentheseSiNegatif, reduireAxPlusB } from '../../lib/outils/ecritures'\nimport { pgcd } from '../../lib/outils/primalite'\nimport { texteGras } from '../../lib/format/style'\nimport Exercice from '../deprecatedExercice.js'\nimport { mathalea2d, colorToLatexOrHTML } from '../../modules/2dGeneralites.js'\nimport { listeQuestionsToContenu, randint } from '../../modules/outils.js'\nimport { min, max } from 'mathjs'\nexport const titre = 'Graphical representation of an affine function'\nexport const dateDeModifImportante = '08/05/2023'\n\n/**\n* @author Stéphane Guyon (mise à jour avec les cas Gilles Mora)\n* 2F10-3\n*/\nexport const uuid = 'c360e'\nexport const ref = '2F10-3'\nexport default function Representerfonctionaffine () {\n  Exercice.call(this)\n  this.titre = titre\n  this.consigne = 'Represent graphically ' + (this.nbQuestions === 1 ? 'the following affine function $f$ defined' : 'the following affine functions $f$ defined') + ' on $\\\\mathbb R$ by:'\n  this.nbQuestions = 3 // On complète le nb de questions\n  this.nbCols = 1\n  this.nbColsCorr = 1\n  this.tailleDiaporama = 3\n  this.video = ''\n  this.spacing = 1\n  this.spacingCorr = 1\n  this.sup = 1\n\n  this.nouvelleVersion = function () {\n    this.sup = parseInt(this.sup)\n    this.listeQuestions = []\n    this.listeCorrections = []\n    let typesDeQuestionsDisponibles = []\n    if (this.sup === 1) {\n      typesDeQuestionsDisponibles = [1]\n    }\n    if (this.sup === 2) {\n      typesDeQuestionsDisponibles = [2]\n    }\n    if (this.sup === 3) {\n      typesDeQuestionsDisponibles = [1, 2]\n    }\n\n    const listeTypeDeQuestions = combinaisonListes(typesDeQuestionsDisponibles, this.nbQuestions)\n    const o = texteParPosition('O', -0.5, -0.5, 'medium', 'black', 1)\n    for (let i = 0, a, b, r, c, d, tA, lA, tB, lB, xA, yA, xB, yB, f, lC, typesDeQuestions, texte, texteCorr, cadre, cadreFenetreSvg, cpt = 0;\n      i < this.nbQuestions && cpt < 50;) { // on rajoute les variables dont on a besoin\n      typesDeQuestions = listeTypeDeQuestions[i]\n      switch (typesDeQuestions) {\n        case 1:\n          {\n            f = (x) => a * x + b\n            a = randint(0, 3, [0]) * choice([-1, 1])// coefficient non nul a de la fonction affine\n            b = randint(0, 3, [0]) * choice([-1, 1])// ordonnée à l'origine b non nulle de la fonction affine\n            f = (x) => a * x + b\n\n            xA = 0\n            yA = f(xA)\n            xB = randint(1, 3) * choice([-1, 1])// Abscisse de B\n            yB = f(xB)// Ordonnée de B\n\n            const A = point(xA, yA, 'A')\n            const B = point(xB, yB, 'B')\n            c = droite(A, B)\n            c.color = colorToLatexOrHTML('red')\n            c.epaisseur = 2\n\n            cadre = {\n              xMin: min(-5, xA - 1, xB - 1),\n              yMin: min(-5, yA - 1, yB - 1),\n              xMax: max(5, xA + 1, xB + 1),\n              yMax: max(5, yA + 1, yB + 1)\n            }\n            // It's weird but it's because in mathAlea, attributes don't have capital letters.\n            // So even when it's the same frame, we have to do it.\n            cadreFenetreSvg = {\n              xmin: cadre.xMin,\n              ymin: cadre.yMin,\n              xmax: cadre.xMax,\n              ymax: cadre.yMax,\n              scale: 0.6\n            }\n\n            r = repere(cadre)\n\n            tA = tracePoint(A, 'red') // Variable qui trace les points avec une croix\n            tB = tracePoint(B, 'red') // Variable qui trace les points avec une croix\n            lA = labelPoint(A, 'red')// Variable qui trace les nom s A et B\n            lB = labelPoint(B, 'red')// Variable qui trace les nom s A et B\n\n            tA.taille = 5\n            tA.epaisseur = 2\n            tB.taille = 5\n            tB.epaisseur = 2\n\n            texte = `$f(x)=${reduireAxPlusB(a, b)}$ <br>`\n            if (a !== 0) {\n              texteCorr = 'We know that the graphic representation of an affine function is a line.<br>'\n              texteCorr += 'It is therefore sufficient to determine the coordinates of two points to be able to represent $f$.<br>'\n              texteCorr += `Since $f(${xA})=${yA}$, we have $A(${xA},${yA}) \\\\in \\\\mathcal{C_f}$.<br>`\n              texteCorr += 'We look for a second point, and we take an antecedent at random:<br>'\n              texteCorr += `Let $x=${xB}$:<br>`\n              texteCorr += `We calculate: $f(${xB})=${a} \\\\times ${ecritureParentheseSiNegatif(xB)}${ecritureAlgebrique(b)}=${yB}$.<br>`\n              texteCorr += `We deduce that $B(${xB},${yB}) \\\\in \\\\mathcal{C_f}$.<br>`\n            } else {\n              texteCorr = 'We observe that $f$ is a constant function.<br>'\n              texteCorr += `Its graphic representation is therefore a straight line parallel to the abscissa axis, with the equation $y=${yA}$.<br>`\n            }\n            texteCorr += mathalea2d(cadreFenetreSvg,\n              lA, lB, r, c, tA, tB, o) }\n          texteCorr += `<br>${texteGras('Noticed')}: to draw the line, we can also use the slope coefficient of the line ($${a}$) and its intercept ($${b}$).<br>`\n          break\n\n        case 2: // cas du coefficient directeur fractionnaire\n          { a = randint(-5, 5, [0]) // numérateur coefficient directeur non nul\n            b = randint(-5, 5, [0]) // ordonnée à l'origine non nulle\n            d = randint(2, 5) // dénominateur coefficient directeur non multiple du numérateur pour éviter nombre entier\n            while (pgcd(a, d) !== 1) {\n              a = randint(-5, 5, [0]) // numérateur coefficient directeur non nul\n              b = randint(-5, 5, [0]) // ordonnée à l'origine non nulle\n              d = randint(2, 5)\n            }\n            f = (x) => a / d * x + b\n            xA = 0 // Abscisse de A\n            yA = f(xA)// Ordonnée de A\n            xB = d\n            yB = f(xB)\n\n            const A1 = point(xA, yA, 'A')\n            const B1 = point(xB, yB, 'B')\n            c = droite(A1, B1)\n            c.color = colorToLatexOrHTML('red')\n            c.epaisseur = 2\n\n            cadre = {\n              xMin: min(-5, xA - 1, xB - 1),\n              yMin: min(-5, yA - 1, yB - 1),\n              xMax: max(5, xA + 1, xB + 1),\n              yMax: max(5, yA + 1, yB + 1)\n            }\n\n            cadreFenetreSvg = {\n              xmin: cadre.xMin,\n              ymin: cadre.yMin,\n              xmax: cadre.xMax,\n              ymax: cadre.yMax,\n              scale: 0.6\n            }\n\n            texte = `$f(x)=${texFractionReduite(a, d)}x ${ecritureAlgebrique(b)}$ <br>`\n\n            texteCorr = 'We know that the graphic representation of an affine function is a line.<br>'\n            texteCorr += 'It is therefore sufficient to determine the coordinates of two points to be able to represent $f$.<br>'\n            texteCorr += `As $f(${xA})=${yA}$, we have: $A(${xA},${yA}) \\\\in \\\\mathcal{C_f}$.<br>`\n            texteCorr += 'We look for a second point, and we take an antecedent which facilitates the calculations:<br>'\n            texteCorr += `For example $x=${xB}$:<br>`\n            texteCorr += `We calculate: $f(${xB})=${texFractionReduite(a, d)} \\\\times ${ecritureParentheseSiNegatif(xB)}${ecritureAlgebrique(b)}=${yB}$.<br>`\n            texteCorr += `We deduce that $B(${xB},${yB}) \\\\in \\\\mathcal{C_f}$.<br>`\n\n            tA = tracePoint(A1, 'red') // Variable qui trace les points avec une croix\n            lA = labelPoint(A1, 'red')// Variable qui trace les nom s A et B\n            tB = tracePoint(B1, 'red') // Variable qui trace les points avec une croix\n            lB = labelPoint(B1, 'red')// Variable qui trace les nom s A et B\n            // lC = labelPoint(f, 'C_f')// Variable which traces the names A and B\n\n            r = repere(cadre)// On définit le repère\n            texteCorr += mathalea2d(\n              cadreFenetreSvg,\n              r, c, tA, lA, tB, lB, lC, o)\n            // We draw the graph\n            texteCorr += `<br>${texteGras('Noticed')}: to draw the line, we can also use the slope coefficient of the line ($${texFractionReduite(a, d)}$) and its intercept ($${b}$).<br>`\n          }\n          break\n      }\n\n      if (this.questionJamaisPosee(i, a, b)) {\n        // If the question has never been asked, we create another one\n        this.listeQuestions.push(texte)\n        this.listeCorrections.push(texteCorr)\n        i++\n      }\n      cpt++\n    }\n    listeQuestionsToContenu(this)\n  }\n  this.besoinFormulaireNumerique = ['Question Types', 3, '1: Integer values\\n2: Fractional values\\n3: Combination of the two previous 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