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二次函数具有轴对称性已是初中知识,三次函数具有中心对称性也逐渐成为高中数学的寻常知识.一般的实系数一元n(n≥4)次多项式函数的对称性如何?它们具有对称性的充要条件是什么?笔者试为探讨并给出结论.首先,根据文献[1][2],给出下面两个重要的定理.1定义域为R的可导函数对称性的充要条件定理1定义域为R的可导函数y=f(x)图象关于点(a,f(a))中心对称的充要条件是它的导函数y=f′(x)图象关于x=a轴对称.
The quadratic function has axial symmetry has been the junior high school knowledge, the cubic function has the center symmetry has also become the common knowledge of high school mathematics.General real coefficient univariate n (n≥4) polynomial function of symmetry how? They have symmetry The author tries to discuss and give the conclusion.Firstly, according to the literature [1] [2], the following two important theorems are given: 1 The necessary and sufficient Conditional Theorem 1 The Definitive Domain of Conductive Function of R y = f (x) The necessary and sufficient condition for the image to be symmetric about the center of point (a, f (a)) is its derivative y = f ’(x) x = a axis symmetry.