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求函数值域是高一数学教材中的一个盲点,但又是一个很重要的内容。要学好函数这一节,除了会求函数的解析式及定义域外,笔者认为补充有关求函数值域的若干种方法相当有必要。要求函数的值域,首先必须明确两点:一点是函数值域的概念,即对于定义域A上的函数y=f(x),其值域是指集合C=|y|y=_f(x),x∈A|;另一点是函数的定义域,对应法则是确定函数的依据。下面将求函数值域的方法作一系统归纳。
Finding the function value range is a blind spot in the mathematics textbooks for senior ones, but it is also a very important content. In order to learn the function well, besides seeking the analytical form and domain of the function, the author thinks that it is necessary to add several methods to find the value range of the function. To request the value range of a function, first of all, two points must be clarified: One is the concept of function value domain, ie, for the function y=f(x) on domain A, the value domain refers to the set C=|y|y=_f ( x), x∈A|; The other point is the domain of the function, and the corresponding rule is the basis for determining the function. The method of finding the function value range is summarized as follows.