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函数是中学数学中最重要的概念之一,它是高中数学的一条主线,是研究由定量到变量的根本途径,也是高考的重要内容。值域是函数现代定义的三要素之一,在函数的求解和运算过程中经常用到。由于常见函数的形式多种多样,如何求函数的值域一直是学生们比较头痛的问题。值域是函数值所在的集合,一旦函数的定义域和对应法则确定了,函数的值域也就随之确定。下面介绍几种常用的求函数值域的方法,重在分析解题思路,着眼在发展学生求同思维的同时,重视学生寻异思维的发展。
The function is one of the most important concepts in middle school mathematics. It is a main line of high school mathematics, and it is the fundamental way to study from quantitative to variable, and it is also an important content of college entrance examination. Range is one of the three elements of the modern definition of functions and is often used in the process of solving and computing functions. Because of the variety of common functions, how to find the range of functions has always been a headache for students. The domain is the set of function values. Once the domain and corresponding rules of the function are defined, the domain of the function is determined. The following describes several common ways to find the value range of a function, focusing on analyzing problem-solving ideas, focusing on the development of students seeking same-sounding thinking while paying attention to the development of students’ quest for different thinking.