Function Machines
Function Machines Revision
Function Machines
A function machine takes an input, applies a series of mathematical operations to it, and then outputs a result. Function machines are quite a common question type, especially in foundation maths papers. There are 3 main types of questions you could be asked.
Make sure you are happy with the following topics before continuing.
Type 1: Input to Output
Here, you will be given an input and a function machine and then asked to produce the output.
Example: A function machine is shown below, what is the output if the input is 10?
![Function Machines Input Output Multiply Subtract](https://mmerevise.co.uk/app/uploads/2020/08/Function-Machines-1.png)
Type 2: Output Back to Input
Here, you will be given an Output, a function machine, and then asked to find the Input which produced it.
Example: A function machine is shown below. What was the input if the output is 48?
![Function Machines Input Output Subtract Multiply](https://mmerevise.co.uk/app/uploads/2020/08/Function-Machines-2.png)
If the output is 48 we need to follow the operations of the function machine in reverse and do the opposite operation.
First we must reverse Operation 2 which is \times 3, this means we must \div \, 3.
48 \div 3 = 16
Next, Operation 1 which is -10, this means we must +10.
16+10 = 26
This shows the input was 26
Type 3: Creating Function Machines
You may be asked to create a function machine from an equation given.
Example: Draw a function machine below so that b = \dfrac{a-3}{5}
Here we have an input of a and an output of b.
We must next look at the order of operations, for this we will use BIDMAS
As this is a fraction the first operation will be a-3
The Second would then be (a-3) \div 5
Using this we can create the function machine shown below.
![Function Machines Input Output Subtract Divide](https://mmerevise.co.uk/app/uploads/2020/08/Function-Machines-3.png)
Example: Function Machines Problems
Inputting 5 into the function machine below would give an output of 4.
Find the value of x in the function machine below.
[2 marks]
![Function Machines Input Output Add Divide Missing Function](https://mmerevise.co.uk/app/uploads/2020/08/Function-Machines-4.png)
So, if we input 5 into the function machine then we must first add \textcolor{orange}3:
5+3=8
Now, the question tells us that the result of dividing 8 by some number gives us 4, so we divide by \textcolor{orange}2 to complete the function machine
x = 2
Function Machines Example Questions
Question 1: Below is a function machine,
a) Work out the output produced by an input of 35.
[1 mark]
b) Work out the input needed to produce an output of 48.
[1 mark]
a) Inputting 35, we first multiply by 3:
35 \times 3 = 105
Then, add 15 to get
105+15=120
b) We must work backwards and do the opposite operations. So, first subtracting 15 from the given output, we get
48-15=33
Then, dividing by 3 we get,
33\div 3=11
Meaning that 11 is the input required to give an output of 48.
Question 2: Below is a function machine.
Work out the output produced by an input of -5
[1 mark]
Inputting -5, we first multiply by -2:
-5\times-2=10
Then, adding 7 we get,
10+7=17
Meaning that -5 is the input required to give an output of 17.
Question 3: Below is a function machine.
Work out the output produced by an input of 3x
[1 mark]
Inputting 3x, we first multiply by \dfrac{1}{2}
3x\times\dfrac{1}{2}=\dfrac{3}{2}x
Then, dividing by 3 we get,
\dfrac{3}{2}x\div3=\dfrac{1}{2}x
Meaning that 3x is the input required to give an output of \dfrac{1}{2}x
Question 4: Below is a function machine. Give two operations that would output 27 from an input of 9
[2 marks]
Two operations are,
Multiplying by 4, so 9 \times 4 = 36
Subtracting 9, so 36 - 9 = 27
Any combination of operations which produce an output of 27 would be a correct answer.
Question 5: Below is a function machine.
When x is input into the function machine, 2x is the output. Find the value of x.
[2 marks]
We have to see what we get if we input x into the function machine. First, multiplying x by 12,
12\times x=12x
Then, subtracting 25 to get
12x-25
This is the output of inputting x but we know the output is equal to 2x, so we are left with the equation
12x-25=2x
Now we can solve this equation for x. Subtracting 2x from both sides, we get
10x-25=0
Adding 25 to both sides, we get
10x=25
Finally, dividing both sides by 10 we find x to be
x=25\div 10=2.5
Function Machines Worksheet and Example Questions
![Site Logo](https://mmerevise.co.uk/app/themes/complete-tuition-theme/dist/assets/img/logos/mme/site-logo.webp)