两类函数图象对称轴的辨析

• 作 者: 沈玉环
• 机 构: 广东省深圳市盐田区田东中学 518000
• 出 处: 数理化学习(高中版)
• 发表日期: 2006年02期
• 关键词: 类函数 函数图 象对 二次函数 变换方法 右移 可由

下面是两个常见的有关函数图象对称的问题: 1．定义在R上的函数y=f(x)满足f(a+ -x)=f(a-x),那么y=f(x)的图象关于直线 _____对称; 2．定义在R上的函数y=f(a+x)与y= f(a-x)的图象关于直线_____对称．这两个问题,外形相似,极易混淆．实际上,第1题是一个函数的自对称问题,答案是关于直线x=a对称;第2题是两个函数的互对称问题,答案是关于直线x=0对称．

The following are two common questions about function image symmetry: The function y=f(x) defined on R satisfies f(a+-x)=f(a-x), then the image of y=f(x) is symmetrical about the straight line _____; The image of the function y=f(a+x) and y=f(a-x) defined on R is symmetrical about the straight line _____. These two problems are similar in shape and are easily confused. In fact, the first question is the self-symmetry problem of a function, the answer is about the straight line x = a symmetry; the second question is the mutual symmetry problem of the two functions, the answer is about the straight line x = 0 symmetry.