Question

下列各函數(shù)中為奇函數(shù)的是（　�。�

A．y=x+3

B．y=x²+x

C．y=x|x|

D．y=-|x|

Answer 1

分析：所給函數(shù)的定義域都是R，關(guān)于原點(diǎn)對(duì)稱，再根據(jù)奇函數(shù)和偶函數(shù)的定義，對(duì)各個(gè)選項(xiàng)中的函數(shù)進(jìn)行判斷．

解答：解：所給函數(shù)的定義域都是R，關(guān)于原點(diǎn)對(duì)稱．
對(duì)于函數(shù)y=x+3，把x換成-x，函數(shù)變?yōu)閥=-x+3，函數(shù)沒有變?yōu)樵瓉淼南喾磾?shù)，故不是奇函數(shù)．
對(duì)于函數(shù)y=x²+x，把x換成-x，函數(shù)變?yōu)閥=x²-x，函數(shù)沒有變?yōu)樵瓉淼南喾磾?shù)，故不是奇函數(shù)．
對(duì)于函數(shù)y=x|x|，把x換成-x，函數(shù)變?yōu)閥=-x|x|，變?yōu)樵瓉淼南喾磾?shù)，故是奇函數(shù)．
對(duì)于函數(shù)y=-|x|，把x換成-x，函數(shù)還是y=-|x|，不變，故函數(shù)是偶函數(shù)．
故選C．

點(diǎn)評(píng)：本題主要考查奇函數(shù)和偶函數(shù)的定義，函數(shù)的奇偶性的判斷方法，屬于基礎(chǔ)題．