函数是中学数学的基础,甬数的性质是高考的一个热点,函数的对称性就是其巾一个重要的知识点,现在,就函数的对称性来做一个研究.一、函数自身的对称性探究定理1.函数y=f(x)的图像关于点A(a,b)对称的充要条件是f(x)+f(2a-x)=2b证明:(必要性)设点P(x,y)是y=f(x)图像上任一点,∵点P(x,y)关于点A Function is the basis of high school mathematics, the nature of the number of Ningbo is a hot college entrance examination, the symmetry of the function is an important knowledge of the towel, now, to do a study on the symmetry of the function. Theorem 1. The necessary and sufficient condition that the image of the function y = f (x) be symmetric about the point A (a, b) is f (x) + f , y) is any point on y = f (x) image, and point P (x, y) is about point A