Function Machines

A function machine shows the relationship between two variables, the input and the output.

Here is a function machine:

Input → × 3 → + 2 → Output

In this function we multiply the input by 3, then we add 2 to give us the output.

If we put 5 into the function machine:
5 × 3 = 15
15 + 2 = 17
The output is 17

Example 1: Here is a function machine.

Input → × 5 → − 6 → Output

a) Work out the output when the input is 8
b) Work out the input when the output is 49

For part a we need to put 8 into the function machine.

8 × 5 = 40
40 − 6 = 34

The output is 34

For part b the output is 49
We can work backwards, doing the opposite of each operation.
The opposite function is called the inverse function.

The opposite of taking 6 away is adding 6
The opposite of multiplying by 5 is dividing by 5

49 + 6 = 55
55 ÷ 5 = 11

An input of 11 out give an output of 49

Example 2: Here is a function machine.

Input → ÷ 2 → + 7 → Output

a) Work out the output when the input is -4
b) Work out the input when the output is 20

For part a we are putting -4 into the function machine.

-4 ÷ 2 = -2
-2 + 7 = 5

The output is 5

For part b the output is 20
We can use the opposite function.

The opposite of adding 7 is taking away 7
The opposite of dividing by 2 is multiplying by 2

20 - 7 = 13
13 × 2 = 26

An input of 26 out give an output of 20