Question

若函數(shù)y=ax+2的圖象與函數(shù)的圖象關(guān)于直線y=x對(duì)稱，則log_ab的值是

1. A.
   -
2. B.
   
3. C.
   1
4. D.
   2

Answer 1

D
分析：在直線y=ax+2上任取一點(diǎn)（x，ax+2），則此點(diǎn)關(guān)于y=x的對(duì)稱點(diǎn)在直線上，將此對(duì)稱點(diǎn)代入可得出關(guān)于a和b的方程組，解出即可．
解答：∵y=ax+2的圖象與的圖象關(guān)于直線y=x對(duì)稱，
∴y=ax+2圖象上任一點(diǎn)P（x，ax+2）關(guān)于y=x對(duì)稱點(diǎn)Q（ax+2，x）必在的圖象上．
故對(duì)一切實(shí)數(shù)x總有，
∴．
則log_ab=則log₂4=2．
故選D．
點(diǎn)評(píng)：本題考查的是一次函數(shù)的圖象與幾何變換，熟知關(guān)于直線y=x對(duì)稱的點(diǎn)的坐標(biāo)特點(diǎn)是解答此題的關(guān)鍵．