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)的圖象上;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)=的圖象及函數(shù)f(x)=-x²-4x(x≤0)的關(guān)于原點(diǎn)對(duì)稱的圖象如圖所示,

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)的圖象上,故函數(shù)f(x)的“友好點(diǎn)對(duì)”有2對(duì),故選C.