## A Function is Special

A function is a type of equation.

A function has **special rules it must follow:**

In a function there can ONLY be ONE output(y) for every input (x).

Just like I stated before, a Function is Special! 🙂

- It must work for
**every** possible input value
- And it has only
**one relationship** for each input value

THIS IS A FUNCTION! THIS IS NOT A FUNCTION!

****Think of the birthday example. Each person can only have 1 birthday, other people might have the same birthday as you but you have only 1. You are like the x (input) value and your birthday the y (output) value.****

### Example: y = x²

FUNCTION

Could also be written as a table:

X: x |
Y: x^{2} |

3 |
9 |

1 |
1 |

0 |
0 |

4 |
16 |

-4 |
16 |

… |
… |

**It is a function**, because:

- Every element in X is related to Y
- No element in X has two or more relationships
- The X values DO NOT repeat

So it follows the rules.

(Notice how both **4** and **-4** relate to **16**, which is allowed since 4 and -4 are two different numbers.)

### Example: This relationship is **not** a function:

NOT A FUNCTION

This is **not a function**, for these reasons:

- Value “3” in X has no Y
- Value “4” in X has no Y
- Value “5” is related to more than one value in Y
- REMEMBER THE X VALUE CANNOT REPEAT

Find more information about functions here.