Question

下列說(shuō)法正確的是（　�。�

• A、函數(shù)y=a^x與y=（

  1

  a

  ）^x圖象關(guān)于x軸對(duì)稱
• B、函數(shù)y=log_ax與y=log

  1

  a

  x圖象關(guān)于y軸對(duì)稱
• C、函數(shù)y=a^x與y=log_ax圖象關(guān)于直線y=x對(duì)稱
• D、函數(shù)y=a^x與y=log_ax圖象關(guān)于y軸對(duì)稱

Answer 1

考點(diǎn)：指數(shù)函數(shù)與對(duì)數(shù)函數(shù)的關(guān)系

專題：函數(shù)的性質(zhì)及應(yīng)用

分析：根據(jù)圖象關(guān)于原點(diǎn)對(duì)稱、圖象關(guān)于x軸對(duì)稱、圖象關(guān)于y軸對(duì)稱、圖象關(guān)于y=x對(duì)稱，分別畫出出各個(gè)函數(shù)圖象，再對(duì)照選項(xiàng)即可得出正確答案．

解答：解：令a=2，分別作出對(duì)應(yīng)的圖象，由圖象可知
對(duì)于選項(xiàng)A，∵函數(shù)y=a^x與y=（

1

a

）^x圖象關(guān)于y軸對(duì)稱，故不正確，
對(duì)于選項(xiàng)B，∵函數(shù)y=log_ax與y=log

1

a

x圖象關(guān)于x軸對(duì)稱，故不正確，
對(duì)于選項(xiàng)C，D∵函數(shù)y=a^x與y=log_ax圖象關(guān)于直線y=x對(duì)稱，故C正確，D不正確．
故選：C，

點(diǎn)評(píng)：本題主要考查函數(shù)的圖象的對(duì)稱性的應(yīng)用，考查了命題的真假判斷與應(yīng)用，屬于基礎(chǔ)題．