浅析抽象函数的性质

A Brief Discussion on the Properties of Abstract Function

抽象函数是指没有给出具体的函数解析式或图像,只给出一些函数符号及其满足的条件的函数,它是高中函数部分的难点,也是大学高等数学函数部分的一个衔接点,同时,抽象函数能综合函数的概念和性质,又能与数列不等式等巧妙结合。由于抽象函数没有具体的解析表达式作为载体,因此理解研究起来比较困难,所以做抽象函数的题目要求学生基础知识扎实,逻辑推理能力、抽象思维能力、综合应用数学能力较强。下面对抽象函数的性质进行归类整理。

Abstract function refers to the function with only some function symbols and conditions,instead of concrete analytical function or images.It is a difficult point,but it is very important in mathematics learning.Without concrete analytical functions as the carrier,it is hard to understand and research it,so it needs students＇ comprehensive ability in solving problems relating to it.This paper classifies the properties of abstract function.