# What is a function?

Mar 25, 2018

A function is a set of ordered pairs (points) formed from a defining equation, where, for each $x$-value there is only one $y$-value.

#### Explanation:

$x - - - - - - \to y$ represents a function

This means that you can choose an $x$-value and plug it into an equation, usually given as:

$y = \ldots . . \text{ " or" } f \left(x\right) = \ldots . .$

This will give you a $y$-value.

In a function there will be only ONE possible answer for $y$.

If you find you have a choice, then the equation does not represent a function.

The following are functions:

$y = - 3$

$y = 3 x - 5$

$y = 2 {x}^{2} - 3 x + 1$

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

The following are NOT functions:

$x = 3$

$y = \pm \sqrt{x + 20}$