Question

若直角坐標(biāo)平面內(nèi)的兩點(diǎn)滿(mǎn)足條件：①都在函數(shù)的圖像上；②關(guān)于原點(diǎn)對(duì)稱(chēng)，則稱(chēng)點(diǎn)對(duì)是函數(shù)的一對(duì)“友好點(diǎn)對(duì)”（注：點(diǎn)對(duì)與看作同一對(duì)“友好點(diǎn)對(duì)”）．已知函數(shù)，則此函數(shù)的“友好點(diǎn)對(duì)”有（    ）

A．0對(duì)

B．1對(duì)

C．2對(duì)

D．3對(duì)

Answer 1

C

解析試題分析：根據(jù)題意：當(dāng)時(shí)，，則， 當(dāng)函數(shù)為奇函數(shù)時(shí)有，所以函數(shù)的圖象關(guān)于原點(diǎn)對(duì)稱(chēng)的函數(shù)是．由題意作出函數(shù)的圖象，看它與函數(shù)交點(diǎn)個(gè)數(shù)即可得到友好點(diǎn)對(duì)的個(gè)數(shù)．如圖，

觀察圖象可得：它們的交點(diǎn)個(gè)數(shù)是2，即的“友好點(diǎn)對(duì)”有2個(gè)，故選C．
考點(diǎn)：1、創(chuàng)新能力；2、對(duì)數(shù)函數(shù)圖象與性質(zhì)的應(yīng)用；3、二次函數(shù)的圖象及應(yīng)用．