摘 要：不等式是中学数学中的重要内容之一，在几何、代数等多个数学 领域及实际生活中都有广泛运用。同时，不等式与函数之间联系紧密，构造函数 是解不等式和证明不等式的常用方法之一。本文立足函数与不等式的联系，研究 函数背景下的不等式问题。88619

结合教科书和课程标准，本文按照以下三个步骤来研究函数背景下的不等式 问题。首先，选取函数性质中的单调性、零点存在性和凹凸性，研究这些性质中 的不等关系，作为构造函数解不等式问题的理论基础。其次，举例说明解不等式 和证明不等式中镶嵌不等式思想，作为构造函数解不等式问题的思想基础。最后， 将构造函数解不等式问题按照构造方法分类，逐类举例说明，总结方法。根据研 究结论，本文还为教师教学和学生学习提出建议。

毕业论文关键词：不等式；函数；数学学习；教学方法

Inequality Problems under the Background of Functions

Abstract：Inequality is one of the important contents in middle school mathematics。 It has been widely used in many mathematical fields such as geometry

and algebra, as well as real life。 At the same time, the relation between inequality and function is close, and constructing functions is one of the common methods to solve inequalities and prove inequalities。 This paper is based on the relation of function and inequality, studies inequality problems under the background of functions。

Combined with textbooks and curriculum standard, this paper studies inequality problems under the background of functions by the following three steps。 Firstly, select the monotonicity, existence of zero point, concavity and convexity of function properties。 The inequality of these properties is studied as the theoretical basis for constructing functions to solve the inequality problem。 Secondly, giving examples to illustrate that there is inequality thought in solving the inequalities and prove inequalities, and as the ideological basis。 Finally, classify the problem of constructing functions to solve the inequality according to construction method, example by example, and summary method。 According to the research conclusion, this paper puts forward some suggestions for teachers' teaching and students' learning。源Q于D优G尔X论V文Y网wwW.yOueRw.com 原文+QQ75201`8766

Keyword：Inequality; Function; Mathematics learning; Teaching method

目 录

一、 引言 4

(一) 研究背景 4

(二) 研究意义 4

1。 对教师教学的意义 4

2。 对学生解题的意义 4

3。 对学生数学思维培养的意义 5

(三) 研究思路 5

二、 文献研究 5

(一) 函数性质中不等关系的研究 5

(二) 不等式中函数思想的研究 5

(三) 构造函数解不等式问题的研究 6

(四) 文献研究结论 6

三、