Function Machines Questions | Worksheets and Revision | MME

# Function Machines Questions, Worksheets and Revision

Level 4 Level 5

## What you need to know

### 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. Having a good knowledge of the following topics helps

### Example 1: Function Machines

Using the function machine below complete the questions

a)Work out the output we get when we input 7.

b)Work out the input needed to give 11 as an output.

c)Work out the output we get when we input $2x$.

a) As we can see, the function machine applies two operations: “$\times 4$” and “$+1$”, specifically in that order.

So, with 7 as an input, first times by 4:

$7\times 4=28$

Then, subtract 1 to get the answer to be

$28-1=27$

b) To get an input from an output, we have to work backwards, doing the opposite operations in the opposite order.

Working backwards, we can see that the last operation is to subtract 1, so we must add 1 to our given output:

$11+1=12$

Then divide by 4 to give

$12 \div 4 = 3$

CHECK: you can check your answer by putting 3 through the function machine and seeing if the output matches 11.

c) This time, we have to put some algebra into the machine, but the principle is example the same.

Our first operation is multiplying by 4, so we get

$4\times 2x=8x$

Then, subtracting 1 we get

$8x-1$

You can see that we get an expression as an answer, not a number. This is to be expected any time you have to feed algebra through a function machine.

### Example 2: Function Machines

Inputting 5 into the function machine below would give an output of 4.

a)Fill in the missing number in the function machine.

b)Using the function, work out the output produced by an input of $-6$

a) So, if we input 5 into the function machine then we must first add 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 2 to complete the function machine

b) Inputting $-6$, we must first add 3.

$-6+3=-3$

Now we know the second step is to divide by 2, so we get

$-3\div 2=-1.5$

### Example Questions

a) Inputting 35, we first multiply by 3:

$35 \times 3 = 105$

$105+15=120$

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

Inputting -5, we first multiply by -2:

$-5\times-2=10$

$10+7=17$

Meaning that -5 is the input required to give an output of 17

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 $\dfrac{1}{2}x$

Two examples are,

$9\times 3=27$, so one operation would be multiplying by 3.

$9+18=27$, so a second operation would be adding 18.

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

$x=25\div 10=2.5$

### Worksheets and Exam Questions

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