无论在中学还是在大学的数学課程中,函数概念都是一个极为重要的基本概念,然而也是一个困难的概念。学生在接受这一概念时,不是一帆风順的,而总是会感到不易捉摸,从而发生或多或少的各式各样的錯誤观点。造成这种現象的原因是多方面的,不过我认为主要是由于現在所普遍采用的函数概念的定义,虽然是深刻的、正确的,但从某种意义上讲,存在一定的問題。大家熟知,現在普遍采用的函数概念定义一般如下:数值可以任意选择的(有时要在某一个范围内)变量叫作自变量。如果对于自变量的每一个确定的值,另一个变量有确定的值和它对应,那么这个变量叫作 The function concept is an extremely important basic concept in both mathematics courses at the middle school and university, but it is also a difficult concept. When students accept this concept, they are not plain sailing. They always feel elusive, and thus have more or less various misconceptions. There are many reasons for this phenomenon, but I think it is mainly due to the definition of the concept of function that is generally adopted now. Although it is profound and correct, in a certain sense, there are certain problems. It is well known that the commonly used definition of a function concept is generally as follows: A value can be arbitrarily selected (sometimes within a certain range). The variable is called an independent variable. If for each value of the independent variable, the other variable has a certain value that corresponds to it, then this variable is called