# How do you find the domain and the range of the relation, and state whether or not the relation is a function {(4, –6), (3, –6), (–2, 5), (4, 1)}?

Aug 2, 2018

Domain : $- \left\{2 , 3 , 4\right\}$

Range : $\left\{- 6 , 1 , 5\right\}$

Not a function.

#### Explanation:

The domain is also known as the $x$-values and the range is the $y$-values.

Since we know that a coordinate is written in the form $\left(x , y\right)$, all the $x$-values are:
$\left\{4 , 3 , - 2 , 4\right\}$

However, when we write a domain, we typically put the values from least to greatest and do not repeat numbers. Therefore, the domain is:
$- \left\{2 , 3 , 4\right\}$

All the $y$-values are:
$\left\{- 6 , - 6 , 5 , 1\right\}$

Again, put them in least to greatest and do not repeat numbers:
$\left\{- 6 , 1 , 5\right\}$

In a function, each $x -$value can only pair with one $y$-value (each input has a single output). Since there are two "$4$"s in the $x$-values, there are two same $x$-values paired with two different $y$-values, so this relation is not a function.

Hope this helps!