Quiz — 03cparametrees.pdf

Question 1 sur 10 20:00

[{"id":58616,"question":"Soit la fonction f(x) = ax + 3. Si a \u003E 0, alors la fonction est :","option_a":"Croissante","option_b":"Décroissante","option_c":"Constante","option_d":"Non monotone","option_e":"","option_f":"","bonne_reponse":"a","explication":"Si a \u003E 0, la pente de la droite est positive, donc la fonction est 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\": \"Croissante\", \"b\": \"Décroissante\", \"c\": \"Constante\", \"d\": \"Non mo","_debug_options_count":4},{"id":58617,"question":"La fonction f(x) = x² + bx + c admet toujours un sommet dont l'abscisse est donnée par :","option_a":"x = -b\/2a","option_b":"x = b\/2a","option_c":"x = -c\/b","option_d":"x = b\/a","option_e":"","option_f":"","bonne_reponse":"a","explication":"Pour une fonction quadratique f(x) = ax² + bx + c, l'abscisse du sommet est x = -b\/(2a).","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 = -b\/2a\", \"b\": \"x = b\/2a\", \"c\": \"x = -c\/b\", \"d\": \"x = b\/a\"}}","_debug_options_count":4},{"id":58618,"question":"Vrai ou Faux : Le paramètre 'k' dans f(x) = k·e^x ne modifie pas la croissance de la fonction.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"Le paramètre 'k' modifie l'amplitude de la fonction mais pas sa croissance (toujours strictement croissante si k \u003E 0).","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":58619,"question":"Pour la fonction f(x) = (x + m)², si m augmente, alors le sommet de la parabole se déplace :","option_a":"Vers la droite","option_b":"Vers la gauche","option_c":"Vers le haut","option_d":"Vers le bas","option_e":"","option_f":"","bonne_reponse":"b","explication":"Le sommet de f(x) = (x + m)² est en (-m, 0). Si m augmente, -m diminue, donc le sommet se déplace vers la gauche.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"Vers la droite\", \"b\": \"Vers la gauche\", \"c\": \"Vers le haut\", \"d\":","_debug_options_count":4},{"id":58620,"question":"Vrai ou Faux : Dans f(x) = a·sin(x), le paramètre 'a' influence uniquement l'amplitude de la fonction.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Le paramètre 'a' influence à la fois l'amplitude et le signe de la fonction (si a \u003C 0, la fonction est inversée).","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":58621,"question":"La fonction f(x) = log(x + p) est définie pour x \u003E :","option_a":"p","option_b":"-p","option_c":"0","option_d":"1","option_e":"","option_f":"","bonne_reponse":"b","explication":"La fonction logarithme est définie pour x + p \u003E 0, donc x \u003E -p.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"p\", \"b\": \"-p\", \"c\": \"0\", \"d\": \"1\"}}","_debug_options_count":4},{"id":58622,"question":"Vrai ou Faux : Le paramètre 'h' dans f(x) = (x - h)² + k translate la parabole horizontalement et verticalement.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Le paramètre 'h' translate horizontalement (vers la droite si h \u003E 0) et 'k' verticalement (vers le haut si k \u003E 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\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":58623,"question":"Pour la fonction f(x) = a·x³ + b·x², si a \u003C 0 et b \u003E 0, alors la fonction est :","option_a":"Croissante partout","option_b":"Décroissante partout","option_c":"Non monotone","option_d":"Constante","option_e":"","option_f":"","bonne_reponse":"c","explication":"La fonction cubique avec a \u003C 0 et b \u003E 0 n'est pas monotone : elle a un maximum local et un minimum local.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"c\", \"options\": {\"a\": \"Croissante partout\", \"b\": \"Décroissante partout\", \"c\": \"Non mono","_debug_options_count":4},{"id":58624,"question":"Le paramètre 'c' dans f(x) = a·x² + b·x + c représente :","option_a":"L'ordonnée à l'origine","option_b":"Le sommet","option_c":"La pente","option_d":"L'abscisse à l'origine","option_e":"","option_f":"","bonne_reponse":"a","explication":"Le paramètre 'c' est la valeur de f(0), donc l'ordonnée à l'origine de la parabole.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"L'ordonnée à l'origine\", \"b\": \"Le sommet\", \"c\": \"La pente\", \"d\"","_debug_options_count":4},{"id":58625,"question":"Vrai ou Faux : Dans f(x) = tan(x + θ), le paramètre 'θ' décale la fonction horizontalement.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Le paramètre 'θ' dans f(x) = tan(x + θ) décale la fonction horizontalement vers la gauche de θ unités.","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}]