# What is the domain of {(1,2),(2,6),(3,5),(4,6),(5,2)}?

Sep 9, 2015

Domain is $\left\{1 , 2 , 3 , 4 , 5\right\}$

#### Explanation:

For a collection of discrete pairs $\left(\textcolor{red}{x} , \textcolor{b l u e}{f \left(x\right)}\right) \in \left\{\text{some collection of ordered pairs}\right\}$

• The Domain is the collection of $\textcolor{red}{x}$ values
• The Range is the collection of $\textcolor{b l u e}{f \left(x\right)}$ values

$\left(\textcolor{red}{x} , \textcolor{b l u e}{f \left(x\right)}\right) \in \left\{\begin{matrix}\textcolor{red}{1} & \textcolor{b l u e}{2} \\ \textcolor{red}{2} & \textcolor{b l u e}{6} \\ \textcolor{red}{3} & \textcolor{b l u e}{5} \\ \textcolor{red}{4} & \textcolor{b l u e}{6} \\ \textcolor{red}{5} & \textcolor{b l u e}{2}\end{matrix}\right\}$

Sep 9, 2015

The domain is {1,2,3,4,5}

#### Explanation:

The domain of a relation or a function is the set of all first elements in an ordered pair that is in the function.

With the usual naming of pairs as $\left(x , y\right)$, the domain is the collection (set) of all $x$ values.

In notation, the domain of a relation or function $\boldsymbol{\text{R}}$ is:

$\left\{x | \left(\exists y\right) \left(\left(x , y\right) \in \boldsymbol{\text{R}}\right)\right\}$