Chapter 8.1, Problem 15E

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 15E

The given relation is a function.

Explanation of Solution

Given:

A relation:

x	$-2$	$-1$	0	1	2
y	$-3$	$-3$	$-3$	$-3$	$-3$

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.

We know that for a relation to be a function, one x- value cannot have two y -values, while two or more x- values can have same y- value.

Upon looking at our given ordered pairs, we can see that each x- value corresponds to a specific y- value.

Therefore, the given relation is a function.