例谈函数值域求法

Examples on the Methods for Finding the Ranges of Functions

函数值域的求解是一个综合性问题,可以涉及多种思想方法及多个知识点。选择一典型值域问题,通过一题多解即从不同角度审视同一问题,找到解决问题的各具特色的切入点,寻求当前信息和已有的基础知识之间的联系,培养学生综合运用数学思想方法解决问题的能力,促进学生形成一个更加全面、完整的认知结构,对知识结构有深层的、灵活的理解。

The solution of function ranges is a comprehensive problem, which can involve multiple thinking methods and knowledge points. This paper intends to select a typical range problem, to examine the problem from different angles through multiple solutions, to find the distinctive entry points for solving the problem, to seek the connection between the current information and the existing basic knowledge, and to train students to use mathematics comprehensively in problem-solutions. In this way, students can form a more comprehensive and complete cognitive structure, and have a deep and flexible understanding of the knowledge structure.