# How do you know this is a function: (-2,10) (4,1) (9,-4) (3,2) (0,-9)?

Apr 8, 2016

The given points all have different x-coordinates.

#### Explanation:

Recall that a function is a relationship where an inputted number gives only one output number. If there are two or more outputs for a given input, the relationship does not represent a function.

In your case, since each x-coordinate in the given points has only one y-coordinate, these points would represent a function.

However, if there was an added point that had an x-coordinate of any of the given points, the relationship would not represent a function since there would be two points with the $\textcolor{red}{\text{same x-coordinate}}$ but $\textcolor{g r e e n}{\text{different y-coordinate}}$.

For example:

• represents a function
$\left(1 , 5\right) , \left(4 , 3\right) , \left(- 3 , 2\right)$

• does not represent a function
$\left(\textcolor{red}{1} , \textcolor{g r e e n}{5}\right) , \left(4 , 3\right) , \left(\textcolor{red}{1} , \textcolor{g r e e n}{7}\right)$