Symmetry and periodicity of a function are two basic properties of a function. In middle school mathematics, to learn a function, we should first look at the definition domain and value domain, and then study the symmetry (central symmetry, axial symmetry) and periodicity. The symmetry and periodicity of the function and their relationship are often investigated in the college entrance examination. In 2005, the college entrance examination questions in Guangdong and Fujian provinces were divided into big questions and small questions. Let's study some common properties. 1. Symmetry of the function 1. When the function is satisfied, the image of the function is symmetrical about a straight line. It is proved that if any point (x 1, y 1) is taken in the function, then the point (x 1, y 1) is symmetrical with respect to the straight line (y 1), so the point (,y 1) Since the point (x 1, y 1) is any point on the image, the image of the function is symmetrical about the straight line. (Note: Especially when a=b=0, this function is even. )