Chapter 4.6, Problem 25PPE

To determine

To find: whether the relation represented by given table is a function, to state the domain and range.

Answer to Problem 25PPE

The domain $D$ and range $R$ of the function are

  $\begin{array}{l}D=\left\{-4,-1,0,3\right\}\\ R=\left\{-4\right\}\end{array}$

Explanation of Solution

Given information:

Given table:

  

Calculation:

Consider the relation represented by the table

$x$	$-4$	$-1$	0	3
$y$	$-4$	$-4$	$-4$	$-4$

Let us determine whether the given relation is a function, and find the domain and range if the relation is a function.

Step 1: Use the given values of $x$ and $y$ to represent the relation by mapping diagram. The left box represents the $x$ values and the right box represents the $y$ values. The arrows represent the relation between values in the left box with the values in the right hand box.

  

Step 2: From the mapping diagram observe that all the four values of $x$ in the domain are mapped to one value $-4$ in the range. Therefore, by definition, conclude that the relation is a function.

Step 3: The domain $D$ and range $R$ of the function are

  $\begin{array}{l}D=\left\{-4,-1,0,3\right\}\\ R=\left\{-4\right\}\end{array}$