Question

下列函數(shù)為奇數(shù)函數(shù)的是

②

．
①．y=x²； ②y=x³；③y=2^x；④y=log₂x．

Answer 1

分析：據(jù)奇函數(shù)的定義對(duì)四個(gè)選項(xiàng)逐一判斷，①的圖象關(guān)于y軸對(duì)稱故是偶函數(shù)，②根據(jù)奇函數(shù)的定義可判定，③的圖象不關(guān)于原點(diǎn)對(duì)稱，故不符合題意，④y=log₂x的定義域不對(duì)稱，故函數(shù)為非奇非偶函數(shù)．

解答：解：①f（-x）=（-x）²=x²=f（x），∴函數(shù)y=x²為偶函數(shù)
②f（-x）=（-x）³=-x³=-f（x），∴函數(shù)y=x³為奇函數(shù)
③f（-x）=2^-x≠2^x，∴函數(shù)y=2^x不是奇函數(shù)
④y=log₂x的定義域?yàn)閧x|x＞0}，定義域不對(duì)稱，∴函數(shù)y=log₂x為非奇非偶函數(shù)
故答案為：②

點(diǎn)評(píng)：本題主要考查了函數(shù)的奇偶性判斷，解題關(guān)鍵根據(jù)每個(gè)函數(shù)的解析式研究其定義域的對(duì)稱性及函數(shù)圖象的對(duì)稱性進(jìn)行奇偶性的判斷，屬于基礎(chǔ)題．