Chapter 8.1, Problem 5E

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 5E

The given relation is not a function.

Explanation of Solution

Given:

A relation: $(1,2),(1,5),(2,4),(3,3),(4,1)$ .

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 $1$ . We can see that $1$ corresponds to $2\text{ and }5$ .

Therefore, the given relation is not a function.