抽象函数的周期性的证明 ,是学习中的重点和难点 .本文旨在扩大同学们知识面 ,攻破其难点 .共 1 1种类型 .记f(x) 是定义在R上的函数 ,且a b0 .类型 1　若对于任意一个实数x ,都有f(x +a) =f(x +b) ,求证 :函数 y =f(x)是周期函数 .类型 2　若对于任意一个实数x ,都有f(x +a) The periodic proof of the abstract function is the key and difficult point in the study. This paper aims to expand the knowledge of the students and break through the difficulties. There are 11 types. Remember that f(x) is a function defined on R, and a B0. Type 1 For any real number x, there is f(x +a) =f(x +b). Prove that the function y = f(x) is a periodic function. Type 2 If for any real number x, There f(x +a)