Inequalities on Graphs | 图上的不等式

📚 Inequalities on Graphs | 图上的不等式

Interpreting inequalities visually using graphs is a fundamental technique in A-Level Mathematics. It involves sketching the boundary of the inequality and shading the region that satisfies the condition. This topic consolidates your understanding of coordinate geometry, functions, and algebraic manipulation, and it is essential for tackling more advanced concepts such as linear programming and modelling constraints.

利用图形直观地解释不等式是A-Level数学中的一项基本技巧。它包括勾勒不等式的边界并对满足条件的区域进行着色。这个主题巩固了你对坐标几何、函数和代数运算的理解，对于解决更高级的概念（如线性规划与约束建模）至关重要。

1. Understanding Graphical Inequalities | 理解图上的不等式

A graphical inequality on the Cartesian plane divides the plane into two regions: one that satisfies the inequality and one that does not. The division is marked by a boundary, which can be a straight line or a curve, such as a parabola or circle. For inclusive inequalities (using ≤ or ≥), the boundary itself is part of the solution set and is drawn as a solid line. For strict inequalities (< or >), the boundary is not included and must be drawn as a dashed or dotted line.

笛卡尔平面上的图形不等式将平面划分为两个区域：一个满足不等式，另一个不满足。这种划分由边界标记，边界可以是直线或曲线，如抛物线或圆。对于包含不等式（使用≤或≥）的情况，边界本身是解集的一部分，应画成实线。对于严格不等式（<或>），边界不包含在解集内，必须画成虚线或点线。

When you are asked to indicate the region represented by an inequality, you must shade the appropriate side of the boundary. It is conventional to use a light shading or hatching and to label the

Published by TutorHao | A-Level Mathematics Revision Series | aleveler.com

更多咨询请联系16621398022（同微信）