Question

【題目】給出下列命題，其中正確的命題的個(gè)數(shù)（ ）

①函數(shù)圖象恒在軸的下方；

②將的圖像經(jīng)過(guò)先關(guān)于軸對(duì)稱，再向右平移1個(gè)單位的變化后為的圖像；

③若函數(shù)的值域?yàn)?/span>，則實(shí)數(shù)的取值范圍是；

④函數(shù)的圖像關(guān)于對(duì)稱的函數(shù)解析式為

A.1B.2C.3D.4

Answer 1

【答案】C

【解析】

對(duì)于①根據(jù)復(fù)合函數(shù)的單調(diào)性求得最值即可判斷;

對(duì)于②根據(jù)函數(shù)圖像的翻折、平移變化即可判斷;

對(duì)于③根據(jù)對(duì)數(shù)函數(shù)值域?yàn)镽時(shí),判別式滿足的條件,即可求得的取值范圍;

對(duì)于④根據(jù)關(guān)于對(duì)稱的函數(shù)互為反函數(shù),求得反函數(shù)即可判斷.

對(duì)于①函數(shù),由復(fù)合函數(shù)的單調(diào)性判斷方法可知,

函數(shù)在時(shí)單調(diào)遞增,在時(shí)單調(diào)遞減.即在處取得最大值.

所以,所以函數(shù)圖像恒在軸的下方,所以①正確;

對(duì)于②的圖像經(jīng)過(guò)先關(guān)于軸對(duì)稱,可得;再向右平移1個(gè)單位可得,所以②正確;

對(duì)于③函數(shù)的值域?yàn)?/span>,則滿足能取到所有的正數(shù).即滿足,解不等式可得或,所以③錯(cuò)誤.

對(duì)于④函數(shù)的圖像關(guān)于對(duì)稱的函數(shù)為的反函數(shù),根據(jù)指數(shù)函數(shù)與對(duì)數(shù)函數(shù)互為反函數(shù)可知,其反函數(shù)為,所以④正確.

綜上可知,正確的有①②④

故選:C