Quiz — Série fonctions numériques 1 AS.docx

Question 1 sur 10 20:00

[{"id":129773,"question":"Quelle est l'image de 2 par la fonction f(x) = 3x - 5 ?","option_a":"1","option_b":"-1","option_c":"11","option_d":"-11","option_e":"","option_f":"","bonne_reponse":"c","explication":"Pour trouver l'image de 2, on remplace x par 2 dans l'expression de la fonction : f(2) = 3*2 - 5 = 6 - 5 = 1.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"c\", \"options\": {\"a\": \"1\", \"b\": \"-1\", \"c\": \"11\", \"d\": \"-11\"}}","_debug_options_count":4},{"id":129774,"question":"Une fonction affine est toujours représentée par une droite.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Une fonction affine est de la forme f(x) = ax + b, et sa représentation graphique est une droite.","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":129775,"question":"Quel est le domaine de définition de la fonction f(x) = 1\/(x-3) ?","option_a":"R","option_b":"R \\ {3}","option_c":"R \\ {0}","option_d":"R+","option_e":"","option_f":"","bonne_reponse":"b","explication":"La fonction f(x) = 1\/(x-3) n'est pas définie lorsque le dénominateur est nul, c'est-à-dire pour x = 3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"R\", \"b\": \"R \\\\ {3}\", \"c\": \"R \\\\ {0}\", \"d\": \"R+\"}}","_debug_options_count":4},{"id":129776,"question":"La fonction f(x) = x² 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). Ici, f(-x) = (-x)² = x² = f(x), donc la fonction 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":129777,"question":"Quelle est la solution de l'équation f(x) = 0 pour f(x) = 2x - 4 ?","option_a":"x = 2","option_b":"x = -2","option_c":"x = 4","option_d":"x = 0","option_e":"","option_f":"","bonne_reponse":"a","explication":"Pour résoudre f(x) = 0, on pose 2x - 4 = 0, soit 2x = 4, donc x = 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"x = 2\", \"b\": \"x = -2\", \"c\": \"x = 4\", \"d\": \"x = 0\"}}","_debug_options_count":4},{"id":129778,"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 dérivée de f(x) = x³ est f'(x) = 3x², qui est toujours positive ou nulle. La fonction est donc croissante sur 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":129779,"question":"Quel est le sens de variation de la fonction f(x) = -2x + 1 ?","option_a":"Croissante","option_b":"Décroissante","option_c":"Constante","option_d":"Non monotone","option_e":"","option_f":"","bonne_reponse":"b","explication":"Le coefficient directeur de la fonction affine f(x) = -2x + 1 est négatif (-2), donc la fonction est décroissante.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"Croissante\", \"b\": \"Décroissante\", \"c\": \"Constante\", \"d\": \"Non mo","_debug_options_count":4},{"id":129780,"question":"La fonction f(x) = √x est-elle définie pour x = -1 ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"La fonction racine carrée √x n'est définie que pour x ≥ 0. Elle n'est donc pas définie pour x = -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\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":129781,"question":"Quelle est la parité de la fonction f(x) = x³ + x ?","option_a":"Paire","option_b":"Impaire","option_c":"Ni paire ni impaire","option_d":"Constante","option_e":"","option_f":"","bonne_reponse":"b","explication":"Pour vérifier la parité, on calcule f(-x) = (-x)³ + (-x) = -x³ - x = -(x³ + x) = -f(x). La fonction est donc impaire.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"Paire\", \"b\": \"Impaire\", \"c\": \"Ni paire ni impaire\", \"d\": \"Constan","_debug_options_count":4},{"id":129782,"question":"Quel est l'extremum de la fonction f(x) = x² - 4x + 5 ?","option_a":"Minimum en x = 2","option_b":"Maximum en x = 2","option_c":"Minimum en x = -2","option_d":"Maximum en x = -2","option_e":"","option_f":"","bonne_reponse":"a","explication":"La fonction f(x) = x² - 4x + 5 est une parabole tournée vers le haut. Son sommet (minimum) est en x = -b\/(2a) = 4\/2 = 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"Minimum en x = 2\", \"b\": \"Maximum en x = 2\", \"c\": \"Minimum en x = ","_debug_options_count":4}]