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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

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Function machine with input 6 passing through a multiply by 4 box and a subtract 2 box to give output 22, with 24 shown as the intermediate value

A function machine is a quick way to show a rule. The input goes in on the left, each box tells you an operation, and the output comes out on the right.

Follow the arrows in order from left to right. If you change the order, you can get a different answer. In the example shown, input 6 becomes 242424 after multiplying by 4, and then 222222 after subtracting 2. So the machine turns 6 into 22.

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2 marks

Here is a number machine.

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A function machine changes a [     ] into an [     ].

Function Machines Revision Guide

  1. GCSE
  2. /Maths
  3. /Function Machines

Revision notes for Edexcel GCSE Maths Function Machines. Open the guide for explanations and worked examples. Written against the Edexcel GCSE Maths (1MA1) specification, so the content matches what's examinable rather than general Maths background.

Revision guides

Practise questions

1 of 2

A function machine multiplies the input by 555, then adds 999. What is the output when the input is −4-4−4?

Practise questions

1 of 2

A function machine divides the input by 444, then subtracts 333. The output is 555. What was the input?

Practise questions

1 of 2

A function machine divides the input by 333, then adds 888. What is the output when the input is −12-12−12?

Practise questions

1 of 3

A function machine takes an input, multiplies it by 3, and then adds 2. What is the output if the input is 5?