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{"version":3,"file":"2F25-1-MxTrb-Ij.js","sources":["../../src/exercices/2e/2F25-1.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 { segment } from '../../lib/2d/segmentsVecteurs.js'\nimport { latexParCoordonnees, texteParPosition } from '../../lib/2d/textes.js'\nimport { combinaisonListes } from '../../lib/outils/arrayOutils'\nimport { texFractionReduite } from '../../lib/outils/deprecatedFractions.js'\nimport Exercice from '../deprecatedExercice.js'\nimport { mathalea2d } from '../../modules/2dGeneralites.js'\nimport { listeQuestionsToContenu, randint } from '../../modules/outils.js'\nimport { abs } from 'mathjs'\n\nexport const titre = 'Study the parity of a function graphically'\n\n/**\n * Reconnaître la parité d'une fonction\n* @author Stéphane Guyon\n* 2F20\n*/\nexport const uuid = '6e82d'\nexport const ref = '2F25-1'\nexport default function EtudierGraphiqueParite () {\n Exercice.call(this) // Héritage de la classe Exercice()\n this.titre = titre\n this.video = ''\n this.consigne = 'Determine, by graphic reading but by justifying it, whether the function $f$ represented is even, odd or neither even nor odd.'\n this.nbCols = 1\n this.nbColsCorr = 1\n this.spacing = 1\n this.spacingCorr = 1\n this.nbQuestions = 1\n\n this.nouvelleVersion = function () {\n this.listeQuestions = [] // Liste de questions\n this.listeCorrections = [] // Liste de questions corrigées\n let typesDeQuestionsDisponibles = []\n typesDeQuestionsDisponibles = [1, 2, 3, 4, 5, 6]//\n\n const listeTypeDeQuestions = combinaisonListes(typesDeQuestionsDisponibles, this.nbQuestions)\n for (let i = 0, texte, texteCorr, cpt = 0, A, B, s1, s2, s3, s4, a, b, c, f, r, rC, x, C, traceAetB, labA1, labA0, labB0, lA, lB = [], typesDeQuestions; i < this.nbQuestions && cpt < 50;) {\n typesDeQuestions = listeTypeDeQuestions[i]\n const o = texteParPosition('O', -0.3, -0.3, 'medium', 'black', 1)\n switch (typesDeQuestions) {\n case 1:// Cas f(x)=ax+b\n a = randint(-2, 2, [0])\n b = randint(-2, 2, [0])\n r = repere({\n xMin: -5,\n xMax: 5,\n yMin: -5,\n yMax: 5,\n grilleX: false,\n grilleY: false,\n grilleSecondaire: true,\n grilleSecondaireYDistance: 1,\n grilleSecondaireXDistance: 1,\n grilleSecondaireYMin: -5,\n grilleSecondaireYMax: 5,\n grilleSecondaireXMin: -5,\n grilleSecondaireXMax: 5\n })\n rC = repere({\n xMin: -5,\n xMax: 5,\n yMin: -7,\n yMax: 7,\n grilleX: false,\n grilleY: false,\n grilleSecondaire: true,\n grilleSecondaireYDistance: 1,\n grilleSecondaireXDistance: 1,\n grilleSecondaireYMin: -7,\n grilleSecondaireYMax: 7,\n grilleSecondaireXMin: -5,\n grilleSecondaireXMax: 5\n })\n x = randint(-1, 1, [0]) * 2\n f = x => a * x + b\n C = courbe(f, { repere: rC, step: 0.25, color: 'blue' })\n B = point(x, a * x + b)\n A = point(-x, -a * x + b)\n\n labA0 = latexParCoordonnees('-x', -x, 0.8 * (a > 0 ? 1 : -1), 'red', 20, 10, 'white', 8)\n labB0 = latexParCoordonnees('x', x, 0.8 * (a > 0 ? -1 : 1), 'red', 20, 10, 'white', 8)\n lA = latexParCoordonnees('M\\'', -x - 1.1, -a * x + b, 'red', 15, 10, 'white', 6)\n lB = latexParCoordonnees('M', x - 1.1, a * x + b, 'red', 15, 10, 'white', 6)\n labA1 = latexParCoordonnees('f(-x)', 0.5, -a * x + b, 'red', 30, 10, 'white', 8)\n // labB1 = latexByCoordinates('f(x)', -1.5, a * x + b, 'red', 25, 10, 'white', 8)\n traceAetB = tracePoint(A, B, 'red') // Variable qui trace les points avec une croix\n traceAetB.taille = 4\n traceAetB.epaisseur = 2\n\n texte = mathalea2d({ xmin: -5, xmax: 5, ymin: -5, ymax: 5, scale: 0.7 }, r, C, o)\n texteCorr = 'We observe that the graphic representation does not admit the ordinate axis as an axis of symmetry,'\n texteCorr += ' nor the origin as the center of symmetry.<br>'\n texteCorr += `Let us take for example a point $M$ of the curve, with abscissa $${x}$, and`\n texteCorr += ` the point $M'$ also of the curve, but with opposite abscissa: $${-x}$. <br>`\n texteCorr += `The coordinates are $M(${x},${a * x + b})$ and $M'(${-x},${-a * x + b})$. <br>`\n texteCorr += 'We can clearly see that these two points have neither equal nor opposite ordinates.<br>'\n texteCorr += 'The function represented is therefore neither even nor odd.<br>'\n\n texteCorr += mathalea2d({ xmin: -5, xmax: 5, ymin: -7, ymax: 7, scale: 0.7 }, rC, o, C, lA, lB, traceAetB)\n\n break\n case 2:// Cas f(x)=ax\n a = randint(-2, 2, [0])\n r = repere({\n xMin: -5,\n xMax: 5,\n yMin: -5,\n yMax: 5,\n grilleX: false,\n grilleY: false,\n grilleSecondaire: true,\n grilleSecondaireYDistance: 1,\n grilleSecondaireXDistance: 1,\n grilleSecondaireYMin: -5,\n grilleSecondaireYMax: 5,\n grilleSecondaireXMin: -5,\n grilleSecondaireXMax: 5\n })\n\n rC = repere({\n xMin: -5,\n xMax: 5,\n yMin: -7,\n yMax: 7,\n grilleX: false,\n grilleY: false,\n grilleSecondaire: true,\n grilleSecondaireYDistance: 1,\n grilleSecondaireXDistance: 1,\n grilleSecondaireYMin: -7,\n grilleSecondaireYMax: 7,\n grilleSecondaireXMin: -5,\n grilleSecondaireXMax: 5\n })\n\n x = randint(2, 3, [0])\n f = x => a * x\n C = courbe(f, { repere: r, step: 0.25, color: 'blue' })\n\n B = point(x, a * x)\n A = point(-x, -a * x)\n labA0 = latexParCoordonnees('-x', -x - 0.2, 0.8 * (a > 0 ? 1 : -1), 'red', 20, 10, 'white', 8)\n labB0 = latexParCoordonnees('x', x, 0.8 * (a > 0 ? -1 : 1), 'red', 20, 10, 'white', 8)\n lA = latexParCoordonnees('M\\'', -x - 1, -a * x, 'red', 15, 10, 'white', 7)\n lB = latexParCoordonnees('M', x + 1, a * x, 'red', 15, 10, 'white', 7)\n labA1 = latexParCoordonnees('f(-x)=-f(x)', 3, 6, 'red', 90, 10, '', 10)\n\n traceAetB = tracePoint(A, B, 'red') // objet qui contient les croix des points\n s1 = segment(x, a * x, x, 0, 'red')\n s2 = segment(-x, -a * x, -x, 0, 'red')\n s3 = segment(-x, -a * x, 0, -a * x, 'red')\n s4 = segment(x, a * x, 0, a * x, 'red')\n s1.pointilles = 5\n s2.pointilles = 5\n s3.pointilles = 5\n s4.pointilles = 5\n s1.epaisseur = 2\n s2.epaisseur = 2\n s3.epaisseur = 2\n s4.epaisseur = 2\n traceAetB.taille = 4\n traceAetB.epaisseur = 2\n\n texte = mathalea2d({ xmin: -5, xmax: 5, ymin: -5, ymax: 5, scale: 0.7 }, r, C, o)\n texteCorr = 'We observe that the graphic representation admits the origin as the center of symmetry.<br>'\n texteCorr += 'Let us take a point $M$ of the curve, with abscissa $x$, and'\n texteCorr += 'the point $M\\'$ also of the curve, but with opposite abscissa: $-x$. <br>'\n texteCorr += 'The coordinates are $M(x,f(x))$ and $M\\'(-x,f(-x))$. <br>'\n texteCorr += 'We can clearly see that these two points, which have opposite abscissa, also have opposite ordinates.<br>'\n texteCorr += 'The function represented is odd.<br>'\n\n texteCorr += mathalea2d({ xmin: -5, xmax: 6, ymin: -7, ymax: 7, scale: 0.7 }, rC, C, lA, lB, traceAetB, labB0, labA1, s1, s2, s3, s4, labA0)\n break\n case 3:// Cas f(x)=ax^2\n a = randint(-2, 2, [0])\n b = randint(1, 5)\n if (a > 0) { b = -b }\n\n r = repere({\n xMin: -4,\n xMax: 4,\n yMin: -6,\n yMax: 6,\n xUnite: 2,\n yUnite: 1,\n grilleX: false,\n grilleY: false,\n grilleSecondaire: true,\n grilleSecondaireYDistance: 1,\n grilleSecondaireXDistance: 1,\n grilleSecondaireYMin: -6,\n grilleSecondaireYMax: 6,\n grilleSecondaireXMin: -4,\n grilleSecondaireXMax: 4\n })\n\n rC = repere({\n xMin: -4,\n xMax: 4,\n yMin: -6,\n yMax: 6,\n xUnite: 2,\n yUnite: 1,\n grilleX: false,\n grilleY: false,\n grilleSecondaire: true,\n grilleSecondaireYDistance: 1,\n grilleSecondaireXDistance: 1,\n grilleSecondaireYMin: -6,\n grilleSecondaireYMax: 6,\n grilleSecondaireXMin: -4,\n grilleSecondaireXMax: 4\n })\n\n x = 1\n f = x => a * x * x + b\n C = courbe(f, { repere: r, color: 'blue' })\n\n B = point(2 * x, a * x * x + b)\n A = point(-2 * x, a * x * x + b)\n labA0 = latexParCoordonnees('-x', -2 * x - 0.2, -0.8, 'red', 20, 10, 'white', 8)\n labB0 = latexParCoordonnees('x', 2 * x, -0.8, 'red', 20, 10, 'white', 8)\n lA = latexParCoordonnees('M\\'', -2 * x - 1, a * x * x + b, 'red', 15, 10, 'white', 7)\n lB = latexParCoordonnees('M', 2 * x + 1, a * x * x + b, 'red', 15, 10, 'white', 7)\n labA1 = latexParCoordonnees('f(-x)=f(x)', 3.5, 4.5, 'red', 80, 10, '', 14)\n traceAetB = tracePoint(A, B, 'red') // objet qui contient les croix des points\n s1 = segment(2 * x, a * x * x + b, 2 * x, 0, 'red')\n s2 = segment(-2 * x, a * x * x + b, -2 * x, 0, 'red')\n s3 = segment(-2 * x, a * x * x + b, 0, a * x * x + b, 'red')\n s4 = segment(2 * x, a * x * x + b, 0, a * x * x + b, 'red')\n s1.pointilles = 5\n s2.pointilles = 5\n s3.pointilles = 5\n s4.pointilles = 5\n s1.epaisseur = 2\n s2.epaisseur = 2\n s3.epaisseur = 2\n s4.epaisseur = 2\n traceAetB.taille = 4\n traceAetB.epaisseur = 2\n\n texte = mathalea2d({ xmin: -8, xmax: 8, ymin: -6, ymax: 6, scale: 0.7 }, r, C, o)\n texteCorr = 'We observe that the graphic representation admits the ordinates as an axis of symmetry.<br>'\n texteCorr += 'Let us take a point $M$ of the curve, with abscissa $x$, and'\n texteCorr += 'the point $M\\'$ also of the curve, but with opposite abscissa: $-x$. <br>'\n texteCorr += 'The coordinates are $M(x,f(x))$ and $M\\'(-x,f(-x))$. <br>'\n texteCorr += 'We can clearly see that these two points, which have opposite abscissa, have equal ordinates.<br>'\n texteCorr += 'The function represented is even.<br>'\n\n texteCorr += mathalea2d({ xmin: -8, xmax: 8, ymin: -6, ymax: 6, scale: 0.7 }, rC, o, C, lA, lB, traceAetB, labB0, labA1, s1, s2, s3, s4, labA0)\n break\n case 4:// Cas f(x)=a(x-b)²+c\n a = randint(-1, 1, [0]) * 0.5\n b = randint(-3, 3, [0])\n c = randint(1, 3)\n if (a > 0) { c = -c }\n r = repere({\n xMin: -6,\n xMax: 6,\n yMin: -5,\n yMax: 5,\n xUnite: 1,\n yUnite: 1,\n grilleX: false,\n grilleY: false,\n grilleSecondaire: true,\n grilleSecondaireYDistance: 1,\n grilleSecondaireXDistance: 1,\n grilleSecondaireYMin: -5,\n grilleSecondaireYMax: 5,\n grilleSecondaireXMin: -6,\n grilleSecondaireXMax: 6\n })\n\n rC = repere({\n xMin: -6,\n xMax: 6,\n yMin: -8,\n yMax: 8,\n xUnite: 1,\n yUnite: 1,\n grilleX: false,\n grilleY: false,\n grilleSecondaire: true,\n grilleSecondaireYDistance: 1,\n grilleSecondaireXDistance: 1,\n grilleSecondaireYMin: -8,\n grilleSecondaireYMax: 8,\n grilleSecondaireXMin: -6,\n grilleSecondaireXMax: 6\n })\n x = 4 - abs(b)\n f = x => a * (x - b) * (x - b) + c\n C = courbe(f, { repere: rC, step: 0.25, color: 'blue' })\n\n B = point(x, a * (x - b) * (x - b) + c)\n A = point(-x, a * (-x - b) * (-x - b) + c)\n lA = latexParCoordonnees('M\\'', -x - 1, a * (-x - b) * (-x - b) + c, 'red', 15, 10, 'white', 7)\n lB = latexParCoordonnees('M', x + 1, a * (x - b) * (x - b) + c, 'red', 15, 10, 'white', 7)\n // labA1 = latexByCoordinates('f(-x)', 1.2, a * (x - b) * (x - b) + c, 'red', 30, 10, '', 8)\n // labB1 = latexByCoordinates('f(x)', -2, a * (x - b) * (x - b) + c + 0.2, 'red', 25, 10, '', 8)\n traceAetB = tracePoint(A, B, 'red') // objet qui contient les croix des points\n\n traceAetB.taille = 4\n traceAetB.epaisseur = 2\n\n texte = mathalea2d({ xmin: -6, xmax: 6, ymin: -5, ymax: 5, scale: 0.6 }, r, C, o)\n texteCorr = 'We observe that the graphic representation does not admit the ordinate axis as an axis of symmetry,'\n texteCorr += ' nor the origin as the center of symmetry.<br>'\n texteCorr += `Let us take for example a point $M$ of the curve, with abscissa $${x}$, and`\n texteCorr += ` the point $M'$ also of the curve, but with opposite abscissa: $${-x}$. <br>`\n texteCorr += `The coordinates are $M(${x},${a * (x - b) * (x - b) + c})$ and $M'(${-x},${a * (-x - b) * (-x - b) + c})$. <br>`\n texteCorr += 'We can clearly see that these two points have neither equal nor opposite ordinates.<br>'\n texteCorr += 'The function represented is therefore neither even nor odd.<br>'\n\n texteCorr += mathalea2d({ xmin: -6, xmax: 6, ymin: -8, ymax: 8, scale: 0.6 }, rC, o, C, lA, lB, traceAetB)\n break\n case 5:// Cas f(x)=1/ax+b\n a = randint(-2, 2, [0])\n b = randint(-3, 3, [0])\n c = Math.trunc(-b / a)\n r = repere({\n xMin: -6,\n xMax: 6,\n yMin: -5,\n yMax: 5,\n xUnite: 1,\n yUnite: 1,\n grilleX: false,\n grilleY: false,\n grilleSecondaire: true,\n grilleSecondaireYDistance: 1,\n grilleSecondaireXDistance: 1,\n grilleSecondaireYMin: -5,\n grilleSecondaireYMax: 5,\n grilleSecondaireXMin: -6,\n grilleSecondaireXMax: 6\n })\n\n rC = repere({\n xMin: -6,\n xMax: 6,\n yMin: -5,\n yMax: 5,\n xUnite: 1,\n yUnite: 1,\n xLabelMin: 10,\n yLabelMin: 10,\n grilleX: false,\n grilleY: false,\n grilleSecondaire: true,\n grilleSecondaireYDistance: 1,\n grilleSecondaireXDistance: 1,\n grilleSecondaireYMin: -5,\n grilleSecondaireYMax: 5,\n grilleSecondaireXMin: -6,\n grilleSecondaireXMax: 6\n })\n x = randint(-3, 3, [-b / a, 0, 1, -1])\n\n f = x => 1 / (a * x + b)\n C = courbe(f, { repere: r, step: 0.01, color: 'blue' })\n\n B = point(x, 1 / (a * x + b))\n A = point(-x, 1 / (-a * x + b))\n lA = texteParPosition('$M\\'$', -x + (a > 0 ? -1 : 1), 1 / (-a * x + b) + (a > 0 ? 0.5 : -0.5), 'medium', 'red', 1.5)\n lB = texteParPosition('$M$', x - (a > 0 ? -1 : 1), 1 / (a * x + b) + (a > 0 ? 0.5 : -0.5), 'medium', 'red', 1.5)\n\n traceAetB = tracePoint(A, B, 'red') // objet qui contient les croix des points\n\n traceAetB.taille = 4\n traceAetB.epaisseur = 2\n\n texte = mathalea2d({ xmin: -6, xmax: 6, ymin: -5, ymax: 5, scale: 0.7 }, r, C, o)\n texteCorr = 'We observe that the graphic representation does not admit the ordinate axis as an axis of symmetry,'\n texteCorr += ' nor the origin as the center of symmetry.<br>'\n texteCorr += `Let us take for example a point $M$ of the curve, with abscissa $${x}$, and`\n texteCorr += ` the point $M'$ also of the curve, but with opposite abscissa: $${-x}$. <br>`\n texteCorr += `The coordinates are $M(${x},${texFractionReduite(1, a * x + b)})$ and $M'(${-x},${texFractionReduite(1, -a * x + b)})$. <br>`\n texteCorr += 'We can clearly see that these two points have neither equal nor opposite ordinates.<br>'\n texteCorr += 'The function represented is therefore neither even nor odd.<br>'\n\n texteCorr += mathalea2d({ xmin: -6, xmax: 6, ymin: -5, ymax: 5, scale: 0.6 }, rC, o, C, lA, lB, traceAetB)\n break\n case 6:// Cas f(x)=1/ax\n a = randint(-3, 3, [0, 1, -1])\n r = repere({\n xMin: -4,\n xMax: 4,\n yMin: -5,\n yMax: 5,\n xUnite: 2,\n yUnite: 1,\n grilleX: false,\n grilleY: false,\n grilleSecondaire: true,\n grilleSecondaireYDistance: 1,\n grilleSecondaireXDistance: 1,\n grilleSecondaireYMin: -5,\n grilleSecondaireYMax: 5,\n grilleSecondaireXMin: -4,\n grilleSecondaireXMax: 4\n })\n rC = repere({\n xMin: -4,\n xMax: 4,\n yMin: -5,\n yMax: 5,\n xUnite: 2,\n yUnite: 1,\n xLabelMin: 10,\n yLabelMin: 10,\n grilleX: false,\n grilleY: false,\n grilleSecondaire: true,\n grilleSecondaireYDistance: 1,\n grilleSecondaireXDistance: 1,\n grilleSecondaireYMin: -5,\n grilleSecondaireYMax: 5,\n grilleSecondaireXMin: -4,\n grilleSecondaireXMax: 4\n })\n x = 2\n f = x => 1 / (a * x)\n C = courbe(f, { repere: r, step: 0.01, color: 'blue' })\n\n B = point(2 * x, 1 / (a * x))\n A = point(-2 * x, -1 / (a * x))\n labA0 = texteParPosition('$-x$', -2 * x - 0.2, -0.8, 'medium', 'red', 1)\n // labA0 = latexByCoordinates('-x', -2*x - 0.2, -0.8, 'red', 20, 10, 'white', 8)\n labB0 = texteParPosition('$x$', 2 * x - 0.2, -0.8, 'medium', 'red', 1)\n // labB0 = latexByCoordinates('x', 2 * x, -0.8, 'red', 20, 10, 'white', 8)\n lA = texteParPosition('$M\\'$', 2 * (-x) - 0.2, 0.5, 'medium', 'red', 1)\n // lA = latexByCoordinates('M\\'', 2 * (-x), -1 / (a * x), 'red', 15, 10, 'white', 7)\n lB = texteParPosition('$M$', 2 * (x) - 0.2, 0.5, 'medium', 'red', 1)\n // lB = latexByCoordinates('M', 2 * (x), 1 / (a * x), 'red', 15, 10, 'white', 7)\n labA1 = latexParCoordonnees('f(-x)=-f(x)', 3, 3, 'red', 80, 10, '', 14)\n traceAetB = tracePoint(A, B, 'red') // objet qui contient les croix des points\n s3 = segment(-2 * x, -1 / (a * x), 0, 0, 'red')\n s4 = segment(2 * x, 1 / (a * x), 0, 0, 'red')\n s3.pointilles = 5\n s4.pointilles = 5\n s3.epaisseur = 2\n s4.epaisseur = 2\n traceAetB.taille = 4\n traceAetB.epaisseur = 2\n\n texte = mathalea2d({ xmin: -8, xmax: 8, ymin: -5, ymax: 5, scale: 0.7 }, r, C, o)\n texteCorr = 'We observe that the graphic representation admits the ordinates as an axis of symmetry.<br>'\n texteCorr += 'Let us take a point $M$ of the curve, with abscissa $x$, and'\n texteCorr += 'the point $M\\'$ also of the curve, but with opposite abscissa: $-x$. <br>'\n texteCorr += 'The coordinates are $M(x,f(x))$ and $M\\'(-x,f(-x))$. <br>'\n texteCorr += 'We can clearly see that these two points, which have opposite abscissa, have equal ordinates.<br>'\n texteCorr += 'The function represented is odd.<br>'\n\n texteCorr += mathalea2d({ xmin: -8, xmax: 8, ymin: -5, ymax: 5, scale: 0.7 }, rC, C, lA, lB, o, traceAetB, labB0, labA1, s3, s4, labA0)\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 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