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构造法解题是一种辅助手段,通过构造适当的辅助量(如图形、模型、函数等)转化命题形式,以帮助解题.其中构造函数是数学中经常使用的方法,大致来说,其基本想法是:通过构造适当的函数来转化问题,以利用所作函数的图象与性质来帮助论证或求解.文[1]给出构造辅助函数的方法有:直接观察法,作差或作商法,恒等变形法,局部构造,变量分离、以及其它方法.本文将以2013年部分省市高考的函数压轴题为载体,通过具体实例,给出构造函数的方法,并且归纳总结每种方法所能解决的一类问题.
Constructor problem solving is a kind of auxiliary measure, which can be used to help solve the problem by constructing appropriate auxiliary quantities (such as graphics, models, functions, etc.), among which constructor is a commonly used method in mathematics. Generally speaking, The basic idea is to help transform the problem by constructing appropriate functions to take advantage of the image and nature of the function being used to help justify or solve the problem. [1] The methods of constructing auxiliary functions are given by direct observation, , Constant deformation method, local structure, variable separation, and other methods.This paper will be based on the 2013 part of the provincial college entrance examination of the function of the finale as a carrier, through concrete examples, given the constructor method, and summarizes each method A type of problem that can be solved.