Q. 18 - Precalculus Enhanced with Graphing Utilities

Question

Graph each inequality by hand. 

$x^2+y^2\le 9$

Step-by-Step Solution

Answer

The required graph is

Step 1. Given Information

We are given the inequality $x^2+y^2\le 9$ and we need to graph it.   

Step 2. Plotting the graph

First, we plot the equation of the circle $x^2+y^2=9$ with center $\left(0,0\right)$ and radius $3$.

The graph of the inequality $x^2+y^2\le 9$ is a solid circle and so is part of the graph of the inequality. Since $\left(0,0\right)$ satisfies the inequality, the graph consists of the portion towards the origin. The shaded portion represents the inequality. All the points on and inside the circle satisfy the inequality. The graph is