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

Jun 30, 2016

The given set is a function
with a domain of $\left\{1 , 2 , 3 , 4\right\}$
and a range of $\left\{3\right\}$

#### Explanation:

A set $\left\{\begin{matrix}1 & 3 \\ 2 & 3 \\ 3 & 3 \\ 4 & 3\end{matrix}\right\}$
can be considered to be a relation $\textcolor{red}{x} \rightarrow \textcolor{b l u e}{y}$
with $\left(\textcolor{red}{x} , \textcolor{b l u e}{y}\right) \in \left\{\begin{matrix}\textcolor{red}{1} & \textcolor{b l u e}{3} \\ \textcolor{red}{2} & \textcolor{b l u e}{3} \\ \textcolor{red}{3} & \textcolor{b l u e}{3} \\ \textcolor{red}{4} & \textcolor{b l u e}{3}\end{matrix}\right\}$

The domain is the collection of values associated with $\textcolor{red}{x}$ within this relationship, namely $\left\{\textcolor{red}{1 , 2 , 3 , 4}\right\}$

The range is the collection of values associated with $\textcolor{b l u e}{y}$ within this relationship, namely$\left\{\textcolor{b l u e}{3}\right\}$

The relationship is a function if no values of $\textcolor{red}{x}$ are each associated with more than one value of $\textcolor{b l u e}{y}$. (Note that the inverse is not necessarily true; a single value of $\textcolor{b l u e}{y}$ may have more than one corresponding value of $\textcolor{red}{x}$).