Chapter 9.5, Problem 10MRE

To determine

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

Answer to Problem 10MRE

Relation is NOT a function

Explanation of Solution

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

Calculation:

Relation is given as follows:

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

When $y=-1$

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

When $y=-2$

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

When $y=0$

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

When $y=1$

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

When $y=2$

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

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 exists a vertical line that intersects the graph twice.

Thus, the relation is NOT a function.

Conclusion:

Hence, graph of equation is sketched and given relation is NOT a function.