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函数是描述客观世界变化规律的重要数学模型,而自变量是函数中最基本的概念之一。许多函数中的概念和性质都与自变量存在着极为密切的关系。然而,自变量的重要性并没能引起学生足够的重视,以致在处理函数问题时屡屡碰壁。本文首先区别了自变量和因变量,并给出自变量的本质特征,指出无论是简单函数还是复合函数,它们都是关于自变量的函数,函数中的许多疑难问题都可利用自变量得以完美解决。然后通过实例,展示自变量的重要作用。
Function is an important mathematical model to describe the changing law of the objective world, while the argument is one of the most basic concepts in the function. The concept and nature of many functions are closely related to the independent variables. However, the importance of the independent variables did not attract sufficient attention from students, so they often ran into trouble when dealing with function problems. This paper first distinguishes the independent variables from the dependent variables and gives the essential characteristics of the independent variables. It points out that no matter simple functions or complex functions, they are all functions of independent variables. Many difficult problems in the functions can be solved by using independent variables . Then, through examples, show the important role of independent variables.