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函数与方程思想是最重要的一种数学思想,在历年高考中所占比重较大,特别是高考解答题中常渗透函数与方程思想方法.函数思想是指运用运动变化的观点,分析和研究数学中的数量关系,通过建立函数关系(或构造函数)运用函数的图像和性质去分析问题、转化问题和解决问题;方程思想,是从问题的数量关系入手,运用数学语言将问题转化为方程或不等式模型去解决问题。利用转化思想我们还可进行函数与方程间的相互转化。如研究方程、不等式、数列、解析几何等其他内容,一直是高考的热点、重点内容。以下举一些例子说明函数与方程思想体现在各知识点中。
Function and equation thinking is the most important kind of mathematical thought, accounting for a large proportion of the college entrance examination over the years, especially in the college entrance examination answer questions often infiltration function and method of thinking. Function thinking refers to the use of sports change point of view, analysis and study of mathematics In the relationship between the number of functions through the establishment of relations (or constructor) using the image and the nature of the function to analyze the problem, the problem transformation and problem solving; the idea of the equation is to start with the relationship between the number of questions, the use of mathematical language to translate the problem into equation or Inequality model to solve the problem. We can also use the transformation of ideas and functions can be transformed between equations. Such as research equations, inequality, sequence, analytic geometry and other content, has been the hot college entrance examination, the key content. Here are some examples to illustrate the idea of function and equation embodied in the various knowledge points.