# How do you find the domain and range and determine whether the relation is a function given {(-2.5,1), (-1,-1), (0,1), (-1,1)}?

Aug 2, 2018

Domain: $\left\{- 2.5 , - 1 , 0\right\}$

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

This relation is 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 $\left(x , y\right)$, the $x$-values are:
$\left\{- 2.5 , - 1 , 0 , - 1\right\}$

However, when we write a domain or range, we typically put the values from least to greatest and do not repeat numbers. Therefore, the domain is:
$\left\{- 2.5 , - 1 , 0\right\}$

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

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

In a function, each $x$-value can only pair with one $y$-value (each input has a single output). Since there are two $- 1$s in the $x$-values pairing with different $y$-values, this relation is NOT a function.

Hope this helps!