对称在数学中广泛存在,用现代数学语言来讲,对称就是数学对象在某种变换下保持的不变性。在数学中大量的函数图像具有对称性,本文着重研究一类含有相同指数式的分式函数的对称性问题.一、命题引领命题:若f(x)+f(2a-x)=2b,则函数y=f(x)的图像关于点(a,b)对称。证明:设P(x,y)为函数y=f(x)的图像上任意一点,则 Symmetry exists widely in mathematics. In modern mathematics, symmetry is the invariability of mathematical objects under some transformation. In mathematics, a large number of function images have symmetry. In this paper, we study the symmetry problems of a class of fractional functions with the same exponential type. I. Proposition leads the proposition: if f (x) + f (2a-x) = 2b, The image of the function y = f (x) is symmetric about the point (a, b). Proof: Let P (x, y) be an arbitrary point on the image y = f (x)