Chapter 1.2, Problem 38E

To determine

To state: relation by making table of values and graph ordered pairs of relation.

Answer to Problem 38E

  $\left\{\left(-2,6\right),\left(-1,3\right),\left(0,0\right),\left(1,3\right),\left(2,6\right),\left(3,9\right)\right\}$

  

Explanation of Solution

Given information: The relation is as follows:

  $\begin{array}{l}y=|-3x|\\ -2\le x\le 3\\ x\text{ is an integer}\text{.}\end{array}$

Calculation:

Substitute $x=-2,-1,0,1,2,3$ in $y=|-3x|$ to solve corresponding value of y as follows:

  $\begin{array}{l}y=|-3x|\\ y=|-3\left(-2\right)|=\left|6\right|=6\\ y=|-3\left(-1\right)|=\left|3\right|=3\\ y=|-3\left(0\right)|=\left|0\right|=0\\ y=|-3\left(1\right)|=|-3|=3\\ y=|-3\left(2\right)|=|-6|=6\\ y=|-3\left(3\right)|=|-9|=9\end{array}$

Create a table of values for (x,y )as follows:

x	y
-2	6
-1	3
0	0
1	3
2	6
3	9

Thus, the relation is $\left\{\left(-2,6\right),\left(-1,3\right),\left(0,0\right),\left(1,3\right),\left(2,6\right),\left(3,9\right)\right\}$.

Now, plot the values of the relation in the graph as follows: