# Piecewise Functions

## A Function Can be in Pieces

You can create functions that behave differently depending on the input (x) value.

A function made up of 3 pieces

### Example: A function with three pieces:

- when x is less than 2, it gives
**x**,^{2} - when x is exactly 2 it gives
**6** - when x is more than 2 and less than or equal to 6 it gives the line
**10-x**

It looks like this:

(a solid dot means "including",

an open dot means "not including")

And this is how you write it:

The Domain is all Real Numbers up to and including 6:

Dom(f) = (-∞, 6] (using Interval Notation)

Dom(f) = {x | x ≤ 6} (using Set Builder Notation)

And here are some example values:

X | Y |
---|---|

-4 | 16 |

-2 | 4 |

0 | 0 |

1 | 1 |

2 | 6 |

3 | 7 |

### Example: Here is another piecewise function:

which looks like: |

## The Absolute Value Function

The Absolute Value Function is a famous Piecewise Function.

It has two pieces:

- below zero:
**-x** - from 0 onwards:
**x**

f(x) = |x|

## The Floor Function

The Floor Function is a very special piecewise function. It has an infinite number of pieces:

The Floor Function