GCSE(F), GCSE(H),

A **function** is the process of changing one value into another. It consists of an **input** value, the function itself, and the **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 values. Note that the function always stays the same:

Input→ | Function(+ 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.

Another way of writing this is f(*x*) = 2*x* + 4. The left hand side is declaring that this is a function, and the right hand side states the function: *multiply by 2 and add 4.*

A function is normally written with a single letter (normally f) followed by a variable (normally *x*) in brackets on the left hand side; and an expression (the function to be applied to the variable) on the right hand side. When a function is *evaluated*, replace the variable with the number: using the above function, f(3) = 2 x 3 + 4 = 10.

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

Answer: 45

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

2. Given a function f(*x*) = *x*^{2} + 4, find the value of f(7).

Answer: 53

f(*x*) = *x*^{2} + 4

f(7) = 7^{2} + 4

= 49 + 4

= 53

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