Question

【題目】定義:若函數(shù)的圖象經(jīng)過變換后所得的圖象對(duì)應(yīng)的函數(shù)與的值域相同，則稱變換是的同值變換，下面給出了四個(gè)函數(shù)與對(duì)應(yīng)的變換：①, 將函數(shù)的圖象關(guān)于直線作對(duì)稱變換；②, 將函數(shù)的圖象關(guān)于軸作對(duì)稱變換；③, 將函數(shù)的圖象關(guān)于點(diǎn)作對(duì)稱變換；④，將函數(shù)的圖象關(guān)于點(diǎn)作對(duì)稱變換.其中是的同值變換的有__________（寫出所有符合題意的序號(hào))

Answer 1

【答案】①③④

【解析】

根據(jù)變換得函數(shù)解析式，再求對(duì)應(yīng)函數(shù)值域，最后根據(jù)值域是否相同作判斷.

①值域?yàn)?/span>，函數(shù)的圖象關(guān)于直線作對(duì)稱變換得值域?yàn)?/span>，所以是同值變換；

②值域?yàn)?/span>，函數(shù)的圖象關(guān)于軸作對(duì)稱變換得值域?yàn)?/span>，所以不是同值變換；

③值域?yàn)?/span>，函數(shù)的圖象關(guān)于點(diǎn)作對(duì)稱變換得值域?yàn)?/span>，所以是同值變換；

④值域?yàn)?/span>，函數(shù)的圖象關(guān)于點(diǎn)作對(duì)稱變換得值域?yàn)?/span>，所以是同值變換；

故答案為：①③④