Question

在下列變換中，能得到函數(shù)y=log₂x圖象的序號(hào)是    ．
①作函數(shù)y=-log₂（-x）圖象關(guān)于原點(diǎn)O對(duì)稱的圖象．
②作函數(shù)y=2^x關(guān)于y軸對(duì)稱的圖象．
③將函數(shù)圖象上點(diǎn)的橫坐標(biāo)縮小到原來的倍，縱坐標(biāo)不變．
④將函數(shù)的圖象向上平移2個(gè)單位．

Answer 1

【答案】分析：由函數(shù)y=f（x）與函數(shù)y=-f（-x）的圖象關(guān)于原點(diǎn)對(duì)稱，函數(shù)y=f（x）與函數(shù)y=f（-x）的圖象關(guān)于y軸對(duì)稱，可判斷①②的真假，由函數(shù)圖象的伸縮和平移變換規(guī)律，可判斷③④的真假
解答：解：①函數(shù)y=f（x）與函數(shù)y=-f（-x）的圖象關(guān)于原點(diǎn)對(duì)稱，故①正確
②函數(shù)y=f（x）與函數(shù)y=f（-x）的圖象關(guān)于y軸對(duì)稱，所以函數(shù)y=2^x關(guān)于y軸對(duì)稱的函數(shù)為y=2^-x故②不正確
③將函數(shù)圖象上點(diǎn)的橫坐標(biāo)縮小到原來的倍得函數(shù)=log₂x，故③正確
④將函數(shù)的圖象向上平移2個(gè)單位得函數(shù)===log₂x，故④正確
故答案為 ①③④
點(diǎn)評(píng)：本題考查了函數(shù)圖象的對(duì)稱性和函數(shù)圖象的伸縮變換、平移變換