函数是高中数学的主线和基础。函数的对称性和周期性是函数的两个基本性质,共同特点是可以由部分函数图象或解析式得到其他部分或整体的函数图象和解析式,利用对称性和周期性往往能更简捷地使问题得到解决,体现了数学之美。本文拟通过函数的对称性及对称性与周期性的联系方面来探讨函数的有关的性质。 Function is the main line and foundation of high school mathematics. The symmetry and periodicity of the function are two basic properties of the function. The common characteristic is that the function image and the resolution of the other part or the whole can be obtained from the partial function image or the resolution, and the use of symmetry and periodicity can often be simpler To solve the problem, reflecting the beauty of mathematics. This article intends to explore the nature of the function through the symmetry of functions and the relationship between symmetry and periodicity.