Question

20．函數(shù)f（x）=1+$\frac{2}{3x}$的圖象與y=g（x）的圖象關(guān)于x軸對(duì)稱，則g（x）=-1-$\frac{2}{3x}$，函數(shù)f（x）與y=h（x）關(guān)于原點(diǎn)對(duì)稱，則h（x）=-1+$\frac{2}{3x}$．

Answer 1

分析 根據(jù)函數(shù)y=f（x）與函數(shù)y=-f（x）的圖象關(guān)于直線x軸對(duì)稱，函數(shù)y=f（x）與函數(shù)y=f（-x）的圖象關(guān)于直線y軸對(duì)稱，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．即可得到答案．

解答 解：函數(shù)f（x）=1+$\frac{2}{3x}$的圖象與y=g（x）的圖象關(guān)于x軸對(duì)稱，
則g（x）=-f（x）=-1-$\frac{2}{3x}$，
函數(shù)f（x）與y=h（x）關(guān)于原點(diǎn)對(duì)稱，
則h（x）=-f（-x）=-1+$\frac{2}{3x}$，
故答案為：-1-$\frac{2}{3x}$，-1+$\frac{2}{3x}$，

點(diǎn)評(píng) 本題主要考查函數(shù)圖象的對(duì)稱變換，一般地，函數(shù)y=f（x）與函數(shù)y=-f（x）的圖象關(guān)于直線x軸對(duì)稱，函數(shù)y=f（x）與函數(shù)y=f（-x）的圖象關(guān)于直線y軸對(duì)稱，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．