Question

下列函數(shù)的圖象經(jīng)過怎樣的變換才能得到y(tǒng)=sinx的圖象:

(1)y=sin(2x+)(x∈R);

(2)y=25sin(23x-)(x∈R).

Answer 1

思路分析：由函數(shù)y=sinx(x∈R)的圖象得到函數(shù)y=Asin(ωx+φ)(A＞0,ω＞0)(x∈R)的圖象的變換步驟逆過來就是其解答.

解:(1)先將函數(shù)y=sin(2x+)(x∈R)上所有點(diǎn)的橫坐標(biāo)伸長到原來的2倍,縱坐標(biāo)不變,得到函數(shù)y=sin(x+)(x∈R)的圖象,再將所得圖象上各點(diǎn)向右平行移動個(gè)單位長度而得到y(tǒng)=sinx(x∈R)的圖象.

(2)先將函數(shù)y=sin(x-)(x∈R)上各點(diǎn)的縱坐標(biāo)伸長到原來的倍,橫坐標(biāo)不變,得到y(tǒng)=sin(x-)(x∈R)的圖象,再將此函數(shù)圖象上各點(diǎn)的橫坐標(biāo)縮短到原來的,縱坐標(biāo)不變,得到函數(shù)y=sin(x-)(x∈R)的圖象;再將所得圖象上所有點(diǎn)向左平行移動個(gè)單位長度得到y(tǒng)=sinx(x∈R)的圖象.