# How do you find the domain and the range of the relation, and state whether or not the relation is a function {(-3,2), (0,3), (1, 4), (1, -6), (6, 4)}?

Feb 27, 2016

the domain is: $\left\{- 3 , 0 , 1 , 6\right\}$
the range is:$\left\{2 , 3 , 4 , - 6 , 4\right\}$
the relation is not a function since it has TWO distinct y values '4' and '-6' for the same x value of '1' .

#### Explanation:

In the relation:
$\left\{\begin{matrix}- 3 & 2 \\ 0 & 3 \\ 1 & 4 \\ 1 & - 6 \\ 6 & 4\end{matrix}\right\}$:
The domain:
Is the set of all the first numbers of the ordered pairs.
In other words, the domain is all of the x-values.
So in this case the domain is:
$\left\{- 3 , 0 , 1 , 6\right\}$
The range:
Is the set of the second numbers in each pair, or the y-values.
So in this case the range is:
$\left\{2 , 3 , 4 , - 6 , 4\right\}$
A relation is a function if it has only One y-value for each x-value.
So in this case the relation is not a function since it has TWO distinct y values '4' and '-6' for the same x value of '1' .