Chapter 8, Problem 1CT

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 1CT

The given relation is not a function.

Explanation of Solution

Given:

A relation:

  $(0,-2),(0,-1),(0,0),(0,1),(0,2)$ .

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 0 corresponds to differenty-values. We can see that 0 corresponds to $-2,-1,0,1\text{ and }2$ .

Therefore, the given relation is not a function.