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奇函数的图会关于原点对称,当函数图象经过平移变换后,函数的对称中心也会发生变化.下面,我们探究一下函数的对称中心.若函数y=f(x)的图象关于点(a,b)对称,则称点(a,b)为函数的对称中心,此时,函数图象上的任意一点P(x,y)关于点(a,b)的对称点Q(2a-x,2b-y)也在图象上;即f(2a-x)+f(x)=2b,或f(2a+x)+f(-x)=2b,或f(a+x)+f(a-x)=2b.对称性的证明:方法一:若f(2a-x)+f(x)=2b,则函数f(x)的图象关于点(a,b)对称;
The graph of odd functions is symmetric about the origin, and the center of symmetry of the function changes when the function image is transformed by translation. Now let’s explore the symmetry center of the function. If the image of the function y = f (x) (a, b) is the symmetric center of the function. At this point, any point P (x, y) on the function image is symmetric about the symmetry point Q (2a f (x) = 2b, or f (2a + x) + f (-x) = 2b or f (a + x) ) + f (ax) = 2b. Proof of Symmetry: Method 1: The image of the function f (x) is symmetric about the point (a, b) if f (2a-x)