Quiz — Série fonctions numériques 1 AS.pdf

Question 1 sur 10 20:00

[{"id":81249,"question":"Quelle est l'image de 2 par la fonction f définie par f(x) = 3x + 1 ?","option_a":"5","option_b":"7","option_c":"6","option_d":"8","option_e":"","option_f":"","bonne_reponse":"b","explication":"Pour calculer l'image de 2 par f, on remplace x par 2 dans l'expression de f : f(2) = 3*2 + 1 = 7.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"5\", \"b\": \"7\", \"c\": \"6\", \"d\": \"8\"}}","_debug_options_count":4},{"id":81250,"question":"La fonction f(x) = x² est-elle croissante sur ℝ ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"La fonction f(x) = x² est décroissante sur ]-∞, 0] et croissante sur [0, +∞[. Elle n'est donc pas croissante sur tout ℝ.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":81251,"question":"Quel est l'antécédent de 4 par la fonction f définie par f(x) = 2x - 3 ?","option_a":"3.5","option_b":"3","option_c":"2.5","option_d":"4","option_e":"","option_f":"","bonne_reponse":"a","explication":"Pour trouver l'antécédent de 4, on résout l'équation 2x - 3 = 4. On obtient 2x = 7, donc x = 3.5.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"3.5\", \"b\": \"3\", \"c\": \"2.5\", \"d\": \"4\"}}","_debug_options_count":4},{"id":81252,"question":"La fonction f(x) = -x + 5 est-elle décroissante sur ℝ ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"La fonction f(x) = -x + 5 a un coefficient directeur négatif (-1), donc elle est décroissante sur tout ℝ.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":81253,"question":"Quelle est la valeur de f(0) pour la fonction f(x) = 4x² - 2x + 1 ?","option_a":"-1","option_b":"1","option_c":"0","option_d":"2","option_e":"","option_f":"","bonne_reponse":"b","explication":"Pour calculer f(0), on remplace x par 0 dans l'expression de f : f(0) = 4*0² - 2*0 + 1 = 1.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"-1\", \"b\": \"1\", \"c\": \"0\", \"d\": \"2\"}}","_debug_options_count":4},{"id":81254,"question":"La fonction f(x) = x³ est-elle croissante sur ℝ ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"La fonction f(x) = x³ est strictement croissante sur tout ℝ car sa dérivée f'(x) = 3x² est toujours positive.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":81255,"question":"Quel est le tableau de variations de la fonction f(x) = -2x + 4 ?","option_a":"\u003Ctable\u003E\u003Ctr\u003E\u003Ctd\u003Ex\u003C\/td\u003E\u003Ctd\u003E-∞\u003C\/td\u003E\u003Ctd\u003E+∞\u003C\/td\u003E\u003C\/tr\u003E\u003Ctr\u003E\u003Ctd\u003Ef(x)\u003C\/td\u003E\u003Ctd\u003E+∞\u003C\/td\u003E\u003Ctd\u003E-∞\u003C\/td\u003E\u003C\/tr\u003E\u003C\/table\u003E","option_b":"\u003Ctable\u003E\u003Ctr\u003E\u003Ctd\u003Ex\u003C\/td\u003E\u003Ctd\u003E-∞\u003C\/td\u003E\u003Ctd\u003E+∞\u003C\/td\u003E\u003C\/tr\u003E\u003Ctr\u003E\u003Ctd\u003Ef(x)\u003C\/td\u003E\u003Ctd\u003E-∞\u003C\/td\u003E\u003Ctd\u003E+∞\u003C\/td\u003E\u003C\/tr\u003E\u003C\/table\u003E","option_c":"\u003Ctable\u003E\u003Ctr\u003E\u003Ctd\u003Ex\u003C\/td\u003E\u003Ctd\u003E-∞\u003C\/td\u003E\u003Ctd\u003E+∞\u003C\/td\u003E\u003C\/tr\u003E\u003Ctr\u003E\u003Ctd\u003Ef(x)\u003C\/td\u003E\u003Ctd\u003E4\u003C\/td\u003E\u003Ctd\u003E-∞\u003C\/td\u003E\u003C\/tr\u003E\u003C\/table\u003E","option_d":"\u003Ctable\u003E\u003Ctr\u003E\u003Ctd\u003Ex\u003C\/td\u003E\u003Ctd\u003E-∞\u003C\/td\u003E\u003Ctd\u003E+∞\u003C\/td\u003E\u003C\/tr\u003E\u003Ctr\u003E\u003Ctd\u003Ef(x)\u003C\/td\u003E\u003Ctd\u003E+∞\u003C\/td\u003E\u003Ctd\u003E4\u003C\/td\u003E\u003C\/tr\u003E\u003C\/table\u003E","option_e":"","option_f":"","bonne_reponse":"a","explication":"La fonction f(x) = -2x + 4 est une fonction affine décroissante (coefficient directeur négatif). Son tableau de variations montre que f(x) tend vers +∞ quand x tend vers -∞ et vers -∞ quand x tend vers +∞.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"\u003Ctable\u003E\u003Ctr\u003E\u003Ctd\u003Ex\u003C\/td\u003E\u003Ctd\u003E-∞\u003C\/td\u003E\u003Ctd\u003E+∞\u003C\/td\u003E\u003C\/tr\u003E\u003Ctr\u003E\u003Ctd\u003Ef(x)\u003C","_debug_options_count":4},{"id":81256,"question":"La fonction f(x) = |x| est-elle paire ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Une fonction est paire si f(-x) = f(x) pour tout x. Ici, f(-x) = |-x| = |x| = f(x), donc f est paire.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":81257,"question":"Quelle est la dérivée de la fonction f(x) = 5x² - 3x + 2 ?","option_a":"10x - 3","option_b":"5x - 3","option_c":"10x² - 3x","option_d":"5x² - 3","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée de f(x) = 5x² - 3x + 2 est f'(x) = 10x - 3 (dérivée de 5x² = 10x, de -3x = -3, et la dérivée de 2 est 0).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"10x - 3\", \"b\": \"5x - 3\", \"c\": \"10x² - 3x\", \"d\": \"5x² - 3\"}}","_debug_options_count":4},{"id":81258,"question":"La fonction f(x) = 1\/x est-elle définie en x = 0 ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"La fonction f(x) = 1\/x n'est pas définie en x = 0 car la division par zéro est impossible.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4}]