類型一冪函數(shù)的概念
[例1] 下列函數(shù):①y=x3;②y=x2+2x;③y=4x2;④y=x5+1;⑤y=(x-1)2;⑥y=x.其中冪函數(shù)的個數(shù)為( B )
A.1 B.2
C.3 D.4
[解析] ②為二次函數(shù),③中系數(shù)不是1,④中解析式為多項式,⑤中底數(shù)不是自變量本身,所以只有①⑥是冪函數(shù),故選B.
冪函數(shù)解析式的結構特征:?1?解析式是單項式;?2?冪指數(shù)為常數(shù),底數(shù)為自變量,系數(shù)為1.
[變式訓練1] (1)已知冪函數(shù)f(x)=k·xα的圖象過點,則k+α=( C )
A. B.1
C. D.2
(2)已知函數(shù)y=(m2+2m-2)xm+2+2n-3是冪函數(shù),則m=-3或1,n=-3或1.
解析:(1)由冪函數(shù)定義知k=1,把代入y=xα得α=,∴k+α=.選C.
(2)因為函數(shù)y=(m2+2m-2)xm+2+2n-3是冪函數(shù),由冪函數(shù)的定義得
解得m=-3或1,n=.