Chapter 4.6, Problem 26PPE

To determine

To make: a table that represents a relation that is not a function and to explain the relation is not a function.

Explanation of Solution

Consider the relation represented by the table

$x$	$-2$	$-1$	1	1
$y$	3	4	5	6

Let us determine whether the relation is a function or not.

Step 1: From the table observe that the $x$ values are $-2,-1,1$ and the $y$ values are 3,4,5,6.

Step 2: Let us now represent the relation by mapping diagram. The left box represents the domain and the right box represents the range. The arrows represent the relation between values in the left box with the values in the right hand box.

  

Step 3: From the mapping diagram observe that the value 1 in the left box is mapped to two different values, namely 5 and 6 in the right box. Therefore, by definition, conclude that the relation is not a function.