# How do you find the domain and range and determine whether the relation is a function given {(4,5), (6,5), (3,5)}?

May 30, 2017

See explanation.

#### Explanation:

If a relation is given as the set of points then:

• the domain is the set of all first ($x$) coordinates of the points. Here we have: $D = \left\{3 , 4 , 6\right\}$

• the range is the set of all second ($y$) coordinates. Here there is only one value of $y$, so rangeis a one element set: $R = \left\{2\right\}$

• to find if a relation is a function you have to find out if all values in the domain occur only once (have only one value)

Here the condition is met, so it is a function.

If there was another value for any of already mentioned arguments (for example if a point $\left(3 , - 1\right)$ was added) then such relation would not be a function because argument $3$ would have $2$ different values: $5$ and $- 1$