Question

下列函數(shù)中，圖象關(guān)于坐標(biāo)原點(diǎn)對(duì)稱的是（ ）
A．y=lg
B．y=cos
C．y=|x|
D．y=sin

Answer 1

【答案】分析：根據(jù)函數(shù)的性質(zhì)可得奇函數(shù)關(guān)于原點(diǎn)對(duì)稱，偶函數(shù)的圖象關(guān)于y軸對(duì)稱，要找圖象關(guān)于原點(diǎn)對(duì)稱，即在4個(gè)選項(xiàng)中找出奇函數(shù)即可，結(jié)合選項(xiàng)利用排除法．
解答：解：根據(jù)函數(shù)的性質(zhì)可得奇函數(shù)關(guān)于原點(diǎn)對(duì)稱，偶函數(shù)的圖象關(guān)于y軸對(duì)稱，
A：y=lgx是非奇非偶函數(shù)，錯(cuò)誤
B：y=cosx為偶函數(shù)，圖象關(guān)于y軸對(duì)稱，錯(cuò)誤
C：y=|x|為偶函數(shù)，圖象關(guān)于y軸對(duì)稱，錯(cuò)誤
D：y=sinx為奇函數(shù)，圖象關(guān)于原點(diǎn)對(duì)稱，正確
故選D
點(diǎn)評(píng)：本題主要考查了函數(shù)奇、偶函數(shù)的性質(zhì)可得奇函數(shù)關(guān)于原點(diǎn)對(duì)稱，偶函數(shù)的圖象關(guān)于y軸對(duì)稱，奇偶函數(shù)的判斷，注意：再判斷函數(shù)的奇偶性時(shí)，不但要檢驗(yàn)f（-x）與f（x）的關(guān)系，更不能漏掉對(duì)函數(shù)的定義域要求對(duì)稱的檢驗(yàn)．