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函数是中学数学教学的主线,是中学数学的核心内容,也是整个高中数学的基础。函数的性质是竞赛和高考的重点与热点,函数的对称性是函数的一个基本性质,利用对称性往往能更简捷地使问题得到解决,对称关系还充分体现了数学之美。本文拟通过函数自身的对称性和不同函数之间的对称性这两个方面来探讨函数与对称有关的性质。
Function is the main line of high school mathematics teaching, is the core content of high school mathematics, but also the basis of high school mathematics. The nature of the function is the focus and hotspot of competitions and college entrance examinations. The symmetry of a function is a basic property of the function. Symmetry can often make the problem be solved more easily and the symmetry relationship fully embodies the beauty of mathematics. In this paper, the symmetry of the function and the symmetry between the different functions are discussed to explore the symmetry-related properties of the function.