Chapter 4.7, Problem 13PPS

To determine

To graph: The inverse of the relation from the given graph.

Explanation of Solution

Given:

The graph of the relation is:

Calculation:

From the graph of the relation, it is observed that the line passes through the points $\left(-4,-3\right)$ , $\left(-2,-2\right)$ , $\left(0,-1\right)$ , $\left(2,0\right)$ and $\left(4,1\right)$ .

Exchange the x and y coordinates to obtain the inverse.

$\begin{array}{c}\left(-4,-3\right)\to \left(-3,-4\right)\\ \left(-2,-2\right)\to \left(-2,-2\right)\\ \left(0,-1\right)\to \left(-1,0\right)\\ \left(2,0\right)\to \left(0,2\right)\\ \left(4,1\right)\to \left(1,4\right)\end{array}$

The inverse is $\left\{\left(-3,-4\right),\left(-2,-2\right),\left(-1,0\right),\left(0,2\right),\left(1,4\right)\right\}$ . Graph the points on the given graph and then draw a line of inverse points as follows: