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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,对称关系不仅广泛存在于数学问题之中,而且利用对称性往往能更简捷地解决问题,对称关系充分体现了数学之美。本文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探讨了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 hot spots of the competition and the college entrance examination. The symmetry of a function is a basic property of a function. Symmetric relations are not only widely found in mathematical problems, but also can be solved more simply and easily by using symmetry. The symmetrical relationship fully embodies the beauty of mathematics. In this paper, the symmetry of the function itself and the symmetry between different functions are discussed.