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所谓抽象函数是指没有给出函数的具体解析式,只给出了一些体现函数特性的式子的一类函数.它所涉及到的知识非常广泛,处理方法也多种多样,因此是高中数学函数部分的难点.因为抽象,学生感觉到看不见摸不着,接受困难.但是这类问题既能全面地考查学生对函数概念和性质的理解以及代数推理和论证能力,又能综合考查学生对数学符号语言的理解和接受能力.对于发展学生的思维能力.尤其是抽象思维能力,培养学生的创新意识,渗透数学思想方法,提高学生的数学素质,起着非常重要的作用,所以备受各地模考、高考的青睐.有关抽象函数的问题很多,本文就两类主要问题进行探讨.
The so-called abstract function refers to a specific analytical formula that does not give a function, and only gives some types of functions that represent the characteristics of the function. It involves a wide range of knowledge, processing methods are also varied, so it is high school mathematics Difficulty in the function part. Because of abstraction, students feel invisible and difficult to accept. However, such questions can not only fully examine students’ understanding of the concept and nature of functions and algebraic reasoning and argumentation ability, but also can comprehensively examine students’ mathematics. The ability to understand and accept symbolic language. To develop students’ thinking ability, especially abstract thinking ability, to cultivate students’ sense of innovation, to infiltrate mathematical thinking methods, and to improve students’ mathematics quality. There are many problems with abstract functions. This paper discusses two main issues.