Chapter 8.1, Problem 16E

To determine

To represent:

The given relation as a graph and as a mapping diagram. Tell whether the given relation is a function. Explain your reasoning.

Answer to Problem 16E

The given relation is not a function.

Explanation of Solution

Given:

A relation:

x	0	$-5$	$-10$	5	$-10$
y	15	$-10$	$-5$	$-15$	20

Calculation:

Upon graphing our given relation, we will get our required graph as shown below:

The mapping diagram of our given relation would look like:

We know that a relationship will be also a function, when each input in the domain has exactly one specific corresponding output.

Upon looking at our given ordered pairs, we can see that each x- value corresponds to a specific y- value except $-10$ as $-10$ corresponds to $-5\text{ and 20}$ .

Therefore, the given relation is not a function.