求出下列函数的解析式:(1)把函数y=sin(x+)的图象向左平移个单位,再将

求出下列函数的解析式:

(1)把函数y=sin(x+)的图象向左平移个单位,再将横坐标伸长到原来的2倍所得函数图象的解析式;

(2)把函数y=3cos(2x-)的图象向右平移个单位,再将横坐标缩短到原来的,所得函数图象的解析式.

答案

思路分析:图象变换的关键是看先平移后伸缩还是先伸缩,对于后者,可利用ωx+φ=ω(x+)来确定平移单位.

:(1)函数y=sin(x+)的图象向左平移个单位,得到函数y=sin[(x+)+]=sin(x+).

再将横坐标伸长到原来的2倍,得函数y=sin(x2+).

(2)函数y=3cos(2x-)的图象向右平移个单位,

得函数y=3cos[2(x-)-]=3cos(2x-).

再将横坐标缩短到原来的12,得函数y=3cos(2·x12-)=3cos(4x-).

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