# Unit 16 Section 2 : Function Machines

In this section we look at how to find the input and output of function machines.
Function machines take a number as INPUT and give another number as OUTPUT.

INPUT
 FUNCTION MACHINE
OUTPUT

## Finding the Output

Look at the function machine below:
 4
 × 5
 ?
To work out the output, we need to take the input and multiply by 5.
This gives an output of 20.

Now look at the double function machine below:
 5
 × 2
 - 1
 ?
This time, we need to multiply the input by 2 and then subtract 1.
This gives an output of 9.

Practice Questions
Work out the output from these two function machines, then click to see whether you are correct.
 12
 ÷ 4
 ?
 7
 - 3
 × 2
 ?

## Finding the Input

Sometimes we will be given the output from a function machine and we need to work out the input.
To do this, we work backwards through the machine, doing the inverse operation at each stage.

Look at the function machine below:
 ?
 × 4
 8
To work out the input, we need to take the output and divide by 4 (the opposite of multiplying by 4).

This gives an input of 2.

Now look at the double function machine below:
 ?
 - 5
 × 3
 6
This time, we need to do the inverse operations from right to left. We divide the output by 3 and then add 5.

This gives an input of 7.

Inverse Operations
The table below shows the inverse (i.e. opposite) operations.

Practice Questions
Work out the input to these two function machines, then click to see whether you are correct.
 ?
 ÷ 3
 3

 ?
 + 2
 × 5
 25

## Exercises

Work out the answers to the questions below and fill in the boxes. Click on the button to find out whether you have answered correctly. If you are right then will appear and you should move on to the next question. If appears then your answer is wrong. Click on to clear your original answer and have another go. If you can't work out the right answer then click on to see the answer.

Question 1
Fill in the output on each of these function machines.
(a)
 4
 + 6
(b)
 3
 × 10
(c)
 10
 - 7
(d)
 14
 ÷ 2
(e)
 21
 ÷ 3
(f)
 100
 × 5

Question 2
Fill in the input on each of these function machines.
(a)
 × 5
 30
(b)
 + 8
 12
(c)
 - 9
 11
(d)
 ÷ 4
 5
(e)
 + 12
 21
(f)
 × 7
 42

Question 3
Fill in the output on each of these double function machines.
(a)
 3
 × 4
 - 7
(b)
 10
 - 8
 × 7
(c)
 8
 - 5
 × 5
(d)
 -2
 × 6
 + 20
(e)
 7
 + 2
 ÷ 3
(f)
 -5
 + 8
 × 9

Question 4
Fill in the input on each of these double function machines.
(a)
 + 1
 × 4
 12
(b)
 + 7
 ÷ 6
 4
(c)
 × 4
 + 9
 37
(d)
 × 9
 - 20
 34
(e)
 ÷ 6
 - 1
 7
(f)
 - 6
 ÷ 7
 9
(g)
 + 8
 × 4
 24
(h)
 × 2
 + 7
 - 3

Question 5
Here is a triple function machine:
 Input
 × 7
 - 5
 ÷ 2
 Output

(a) What is the output if the input is 8?

(b) What is the input if the output is 22?

(c) What is the input if the output is -13?

Question 6
A number is multiplied by 10, and then 6 is added to get 36.
What was the number?

Question 7
Karen asks her teacher, Miss Sharp, how old she is.
Miss Sharp replies that if you double her age, add 7 and then divide by 3, you get 21.
How old is Miss Sharp?
years old

Question 8
Sally is given her pocket money. She puts half in the bank and then spends £3 in one shop and £2.50 in another shop.
She goes home with £1.25.
How much pocket money was she given?
£

Question 9
A bus has its maximum number of passengers when it leaves the bus station.
At the first stop, half of the passengers get off. At the next stop 7 people get on and at the next stop 16 people get off.
There are now 17 people on the bus.
How many passengers were on the bus when it left the bus station?
passengers

Question 10
Prakesh buys a tomato plant. In the first week it doubles its height.
In the second week it grows 8 cm. In the third week it grows 5 cm.
What was the height of the plant when Prakesh bought it if it is now 35 cm in height?
cm

You have now completed Unit 16 Section 2
 Your overall score for this section is Correct Answers You answered questions correctly out of the questions in this section. Incorrect Answers There were questions where you used the Tell Me button. There were questions with wrong answers. There were questions you didn't attempt.
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