Maîtrisez les branches paraboliques : quiz interactif pour Terminale Maths

Question 1 sur 10 10:00

[{"id":67232,"question":"Quelle est la nature de la branche parabolique de la fonction f(x) = (x² + 1)\/x ?","option_a":"Branche parabolique de direction y = x","option_b":"Branche parabolique de direction y = x²","option_c":"Branche parabolique horizontale","option_d":"Aucune branche parabolique","option_e":"","option_f":"","bonne_reponse":"A","explication":"La division euclidienne donne f(x) = x + 1\/x, donc la branche parabolique a pour direction y = x.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":67233,"question":"La fonction f(x) = (2x² + 3x + 1)\/(x + 1) admet une asymptote oblique.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"La division euclidienne donne f(x) = 2x + 1 + (-1)\/(x+1), donc l'asymptote oblique est y = 2x + 1.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":67234,"question":"Quelle est l'asymptote verticale de la fonction f(x) = (x² - 4)\/(x - 2) ?","option_a":"x = 2","option_b":"x = -2","option_c":"x = 0","option_d":"Aucune asymptote verticale","option_e":"","option_f":"","bonne_reponse":"A","explication":"La fonction n'est pas définie en x = 2, donc x = 2 est une asymptote verticale (limite infinie).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":67235,"question":"Pour la fonction f(x) = (3x³ + 2x² - x)\/(x² + 1), quelle est la direction de la branche parabolique ?","option_a":"y = 3x","option_b":"y = 3x + 2","option_c":"y = 3x²","option_d":"Aucune direction","option_e":"","option_f":"","bonne_reponse":"B","explication":"La division euclidienne donne f(x) = 3x + 2 - (3x + 2)\/(x² + 1), donc la direction est y = 3x + 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":67236,"question":"Une fonction rationnelle peut avoir une branche parabolique sans asymptote oblique.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"Une branche parabolique est toujours associée à une asymptote oblique ou une direction asymptotique.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":67237,"question":"Quelle est la limite de f(x) = (x² + 5x + 6)\/(x + 2) quand x tend vers -2 ?","option_a":"0","option_b":"1","option_c":"-1","option_d":"+∞","option_e":"","option_f":"","bonne_reponse":"D","explication":"La fonction n'est pas définie en x = -2 et la limite tend vers +∞ ou -∞ selon le signe de x.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":67238,"question":"Pour f(x) = (x³ + 2x² - 3x)\/(x² + x - 2), quelle est la partie polynomiale de l'asymptote oblique ?","option_a":"x + 1","option_b":"x² + x - 3","option_c":"x + 2","option_d":"x + 3","option_e":"","option_f":"","bonne_reponse":"A","explication":"La division euclidienne donne f(x) = x + 1 + (x - 1)\/(x² + x - 2), donc la partie polynomiale est x + 1.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":67239,"question":"La fonction f(x) = (x² - 1)\/(x - 1) admet une branche parabolique.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"La fonction se simplifie en f(x) = x + 1 (pour x ≠ 1), donc elle admet une branche parabolique de direction y = x + 1.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":67240,"question":"Quelle est l'asymptote horizontale de f(x) = (5x² + 3x - 2)\/(2x² - x + 1) ?","option_a":"y = 5\/2","option_b":"y = 2","option_c":"y = 0","option_d":"Aucune asymptote horizontale","option_e":"","option_f":"","bonne_reponse":"A","explication":"Les coefficients dominants donnent y = 5\/2, donc l'asymptote horizontale est y = 5\/2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":67241,"question":"Pour f(x) = (x⁴ + 2x³ - x)\/(x³ + 1), quelle est la direction de la branche parabolique ?","option_a":"y = x","option_b":"y = x + 2","option_c":"y = x²","option_d":"Aucune direction","option_e":"","option_f":"","bonne_reponse":"B","explication":"La division euclidienne donne f(x) = x + 2 - (2x + 2)\/(x³ + 1), donc la direction est y = x + 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]