Question

已知冪函數(shù)y=xⁿ₁,y=xⁿ₂,y=xⁿ₃,y=xⁿ₄在第一象限內(nèi)的圖象分別是C₁、C₂、C₃、C₄(如下圖),則n₁、n₂、n₃、n₄的大小關(guān)系是(    )

A.n₁＞n₂＞1,n₃＜n₄＜0                             B.n₁＞n₂＞1,n₄＜n₃＜0

C.n₁＞1＞n₂＞0＞n₄＞n₃                            D.n₁＞1＞n₂＞0＞n₃＞n₄

Answer 1

思路解析:本題通過(guò)對(duì)冪函數(shù)圖象的辨識(shí),考查對(duì)冪函數(shù)性質(zhì)的理解與掌握.四個(gè)函數(shù)圖象都過(guò)(1,1)點(diǎn),對(duì)于任意一個(gè)大于1的值,C₁、C₂、C₃、C₄所對(duì)應(yīng)的y值有y₁＞y₂＞y₃＞y₄,∴采用特值法取x=2.∴轉(zhuǎn)化為指數(shù)函數(shù)y=2^x.由指數(shù)函數(shù)性質(zhì)知y=2^x為增函數(shù),∴n₁＞n₂＞n₃＞n₄.用排除法只能選D.

答案:D