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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。
The function is the main thread of middle school mathematics teaching, is the core content of middle school mathematics, and is also the basis of the mathematics of the whole high school. The nature of the function is the focus and hotspot of the competition and the college entrance examination. The symmetry of the function is a basic property of the function. The symmetry relationship is not only widely existing in the mathematics problem, but also the use of symmetry can often make the problem easier to solve. Symmetrical relationship Also fully embodies the beauty of mathematics. In this paper, the properties of function and symmetry are discussed in terms of the symmetry of the function itself and the symmetry between different functions.