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所谓抽象函数,是指没有明确给出函数表达式,只给出它具有的某些特征或性质,并用一种符号表示的函数.研究抽象函数问题的解法,对教师的教学以及学生深刻理解并牢固掌握函数的相关内容有较大的促进作用.抽象函数是由特殊的、具体的函数抽象而得到的,如y=kx(k≠0)满足(fx+y)=(fx)+(fy),那么y=kx就可叫作抽象函数(fx)的“原型”函数.根据抽象函数的结构,联想到已学过的具有相同或相似结构的某类“原型”函数,并由“原型”函数的相关结论,预测、猜想抽象函数可能具有的某种性质使问题获解,我们称这种解决抽象函数问题的方法为“原型”解法.
The so-called abstract function refers to not expressly given the function expression, only given it has some of the characteristics or properties, and use a symbolic representation of the function of the abstract solution to the problem of teaching teachers and students to understand and understand Firmly grasp the relevant content of the function has a greater role in promoting the abstract function is a special, specific function abstraction obtained, such as y = kx (k ≠ 0) satisfy (fx + y) = (fx) + (fy ), Then y = kx can be called the “prototype” function of the abstract function (fx). According to the structure of the abstract function, it is recalled that some type of “prototype” function with the same or similar structure has been learned, By the related conclusion of “prototype” function, we can predict and guess that the abstract function may have some property to solve the problem. We call this method of solving abstract function problem as “prototype ” solution.