Question

若直角坐標(biāo)平面內(nèi)的兩點(diǎn)P，Q滿足條件：①P，Q都在函數(shù)y＝f(x)的圖像上；②P，Q關(guān)于原點(diǎn)對(duì)稱．則稱點(diǎn)對(duì)[P，Q]是函數(shù)y＝f(x)的一對(duì)“友好點(diǎn)對(duì)”(點(diǎn)對(duì)[P，Q]與[Q，P]看作同一對(duì)“友好點(diǎn)對(duì)”)．已知函數(shù)f(x)＝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　函數(shù)f(x)＝的圖像及函數(shù)f(x)＝－x²－4x(x≤0)的圖像關(guān)于原點(diǎn)對(duì)稱的圖像如圖所示．

則A，B兩點(diǎn)關(guān)于原點(diǎn)的對(duì)稱點(diǎn)一定在函數(shù)f(x)＝－x²－4x(x≤0)的圖像上，故函數(shù)f(x)的“友好對(duì)點(diǎn)”有2對(duì)，選C.