# Functions

## What Is a Function?

Functions express a relationship between an input and an output.

If you put a number in to a function, another number will come out.

### Dictionary Definition

The Merriam-Webster dictionary defines a function as "a mathematical correspondence that assigns exactly one element of one set to each element of the same or another set."

A function can be shown as a mapping diagram, where each number in a set of inputs is mapped to a number in a set of outputs.

The mapping diagram shown below represents a function. Notice that there is a predictable relationship between the input and the output. In the example, 1 is added to each input:

## Functions As Equations

Functions are usually expressed as an equation, where the relationship between the input and output is shown.

The equation below shows a function, which will be called **f**.

The equation shows that the output of the function, which is denoted **f(x)** (said as "f of x"), is related to the input of the function, which is denoted **x**.

The function takes the input **x** and adds 1 to it.

## Functions

Functions relate inputs to outputs. An equation is usually used to describe this relationship.

Functions can be thought of as a mapping. An input is mapped to an output. If you put a number in, the function relates it to another number.

In this mini-curriculum, you will learn about functions.

## Plotting Functions

Functions can be plotted on a graph.

The graph shows the relationship between the input (along the horizontal x-axis) and the output (up the vertical y-axis).

In this mini-curriculum, you will learn about plotting functions.

## Composite Functions

Composite functions combine functions, so that the output of one function becomes the input of another.

In this mini-curriculum, you will learn about composite functions.

## Inverse Functions

The inverse of a function reverses that function.

If a function relates an input to an output, the inverse function relates the output back to the input.

In this mini-curriculum, you will learn about inverse functions.