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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。下面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。一、函数自身的对称性探究定理1.函数y=f(x)的图像关于点A(a,b)对称的充要条件是
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 examination. The symmetry of the function is a basic property of the function. Symmetric relation not only exists in the math problem widely, but also can solve the problem more simply by using the symmetry. Also fully reflects the beauty of mathematics. In the following, the symmetry of the function and the symmetry of different functions are discussed to discuss the symmetry-related properties of the function. First, the function of their own symmetry to explore the theorem 1. Function y = f (x) of the image on the point A (a, b) symmetric necessary and sufficient conditions