函数概念的重要性,不仅是学习高等数学的基础,而尤其重要的是:第一,沒有任何一个概念反映現实世界的現象,象函数相关性这个概念似的那么直接和具体,并且体現着現实世界的动态和实际量之間的互相制約性。第二,沒有任何一个概念,象函数相关性这个概念似的,能够体現出近代数学思維的辯証的特征。它告訴我們考虑量的生动的变化无常性,而不是人为的那样死板;考虑量之間的互相制約性,而不是人为的将它們割裂开。因此对学生来說,掌握它的精神和实质是具有头等重要的意义。但是,就現行中学教材关于函数的定义来看,是不能令人十分滿意的。 (一) 現行中学教材的函数定义。 現行教材的函数定义表述为: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 The importance of the concept of functions is not only the basis for learning advanced mathematics, but particularly important is: First, no concept reflects the phenomenon of the real world, as directly and concretely as the concept of functional relevance, and The mutual constraints between the dynamics of the real world and the actual quantity. Second, no concept, like the concept of functional relevance, can reflect the dialectical characteristics of modern mathematical thinking. It tells us to think about the lively volatility of the quantity, rather than being artificially rigid; consider the mutual constraints between quantities rather than artificially split them apart. Therefore, for students, mastering its spirit and essence is of primary importance. However, as far as the definition of the function of the current middle school textbook is concerned, it cannot be very satisfactory. (a) The definition of the function of the current high school textbook. The definition of the function of the current textbook is expressed as: If for each determined value of the independent variable, the other variable has a certain value and it corresponds to