Question

如果函数y=f(x)满足f(a+x)=f(b-x),则函数y=f(x)的图象关于x= 对称.

Answer 1

请看:

(1)点(x,y)关于（a,b)的对称点（2a-x,2b-y)

(2)若y=f(x)满足f(a+x）=f(a-x),则y=f(x)关于x=a对称

(3)若y=f(x)满足f(a-x）=f(x),则y=f(x)关于x=a/2对称

(4)若y=f(x)满足f(a-x）=f(b+x),则y=f(x)关于x=(a+b)/2对称

(5)若y=f(x)满足f(a+x）=-f(a-x),则y=f(x)关于(a,0)对称

(6)若y=f(x)满足f(a+x）=f(a-x),且f(b+x）=f(b-x),则y=f(x)为周期函数,周期为2|a-b|

（7）若y=f(x)满足f(a+x）=f(a-x),且f(b+x）=-f(b-x),则y=f(x)为周期函数,周期为4|a-b|