A **function** changes one value into another. It consists of an **input** value, the function itself, and an **output** value. The function describes how the input is changed to the output. For example, a function may be *add 3:*

if the input is 4

the function is *add 3*, so 4 + 3

to make the output 7.

This can be written as a table to show multiple input values. Note that the function always stays the same. This process is **mapping** the input values to the output values.

Input | Add 3 | Output |

1 | 1 + 3 | 4 |

2 | 2 + 3 | 5 |

3 | 3 + 3 | 6 |

4 | 4 + 3 | 7 |

5 | 5 + 3 | 8 |

Functions may have more than one stage: for example, *multiply by 2, then add 4* has two stages. If the input was 3, then:

input 3 → x 2 (=6) → + 4 (=10) → output 10.

One function is defined as *add 7*. A second function is defined as *add 3*.

What would be the single equivalent function?

Adding 7 to a number then adding 3 is the equivalent of adding 10.

Answer: Add 10.

A function is defined as *add 2, then multiply by 5*. If the input is 7, what is the output?

Input 7 → + 2 (= 9) → x 5 (= 45) → output 45

Answer: 45

See also Substituting into Expressions

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