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函数思想是利用函数的概念、性质和图象去分析问题、转化问题和求解问题,它是一种很重要的数学思想方法,函数是研究变量的变化规律,所以只要有变量的问题就可以利用函数思想。在求解某些数学问题中,根据问题的条件,构想、组合一种新的函数关系,使问题在新的观点下实行转化并利用函数的有关性质解决原问题是一种行之有效的解题手段。即通过构造辅助函数,把原来问题转化为研究辅助函数的性质,并利用函数的单调性、有界性、奇偶性来解决。
Function idea is to use the concept of the function, the nature and the image to analyze, transform and solve the problem, it is a very important mathematical method, the function is to study the variation of variables, so as long as there is a variable problem can be used Function ideas. In solving some mathematical problems, according to the conditions of the problem, the idea of combining a new functional relationship, the problem under the new view of the conversion and the use of the nature of the function to solve the original problem is an effective solution to the problem means. That is, by constructing auxiliary functions, the original problems are transformed into the properties of auxiliary functions, and the monotonicity, boundedness and parity of the functions are used to solve them.