Expressions as Functions

# Expressions as Functions

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) = 2x + 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.

## Examples

1. 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

2. Given a function f(x) = x2 + 4, find the value of f(7).