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

Jun 5, 2016

Domain: $\left\{2 , 3 , 4\right\}$.
Range: $\left\{1 , 2 , 3\right\}$.
Not a function.

#### Explanation:

Given:

$\left(2 , 1\right)$, $\left(3 , 1\right)$, $\left(3 , 2\right)$, $\left(4 , 1\right)$, $\left(4 , 2\right)$, $\left(4 , 3\right)$

The domain is the set of first elements of each pair, namely:

$\left\{2 , 3 , 4\right\}$

The range is the set of second elements of each pair, namely:

$\left\{1 , 2 , 3\right\}$

This relation is not a function.

For example, the pairs $\left(3 , 1\right)$ and $\left(3 , 2\right)$ define conflicting values for $f \left(3\right)$.