Chapter 9.5, Problem 9MRE

To determine

To calculate: To graph the relation and to tell whether the relation is a function or not

Answer to Problem 9MRE

Relation is a function

Explanation of Solution

Given information: Relation is $\left\{\left(x,y\right):y=\left|x\right|\right\}$

Calculation:

Relation is given as follows:

  $\left\{\left(x,y\right):y=\left|x\right|\right\}$

When $x=-1$

  $\begin{array}{l}y=\left|-1\right|\\ y=1\end{array}$

When $x=-2$

  $\begin{array}{l}y=\left|-2\right|\\ y=2\end{array}$

When $x=0$

  $\begin{array}{l}y=\left|0\right|\\ y=0\end{array}$

When $x=1$

  $\begin{array}{l}y=\left|1\right|\\ y=1\end{array}$

When $x=2$

  $\begin{array}{l}y=\left|2\right|\\ y=2\end{array}$

Graph is sketched as follows:

  

In order to validate that the relation is a function or not, draw any vertical line that intersects the graph more than once.

There do not exists a vertical line that intersects the graph more than once.

Thus, the relation is a function.

Conclusion:

Hence, graph of equation is sketched and given relation is a function.