New Zealand
Level 6 - NCEA Level 1

# Functions Machines

Lesson

## Making sausages

If you think of a sausage machine: something goes in, the machine works its magic, and sausages come out the other end! A function machine is a little like that, just with no sausages. We have 3 important things that happen though, just like a sausage machine.

### Function machines

With a function machine, we have:

• something going in (input)
• something happening in the machine (operation)
• something coming out (output)

### Is that all?

Yes! It looks just like this.

Let's watch a video to see how it works and how it can go in reverse as well.

Remember!

A function machine uses three special terms:

• input
• operation
• output (We don't call this the answer)

#### Worked Examples

##### Question 1

Look at this function machine.

 $2$2 $+$+$1$1 ?
1. In the case above, what is the output of the function machine?

2. If the input was changed to $7$7, what would the new output of the function machine be?

##### Question 2

Look at this function machine.

 $5$5 ? $7$7
1. What is the operation of this function machine?

$2$2

A

$7$7

B

$+$+$5$5

C

$+$+$2$2

D

$-$$22 E \times×22 F 22 A 77 B ++55 C ++22 D -$$2$2

E

$\times$×$2$2

F
2. We can reverse the direction of a function machine.

 $5$5 ? $7$7

Now $7$7 is the input and $5$5 is the output.

What is the operation of this function machine now?

$\times$×$2$2

A

$-$$22 B 55 C 22 D ++22 E -$$7$7

F

$\times$×$2$2

A

$-$$22 B 55 C 22 D ++22 E -$$7$7

F

##### Question 3

Look at this function machine.

 ? $+$+$5$5 $12$12
1. In the case above, what is the input of the function machine?

2. If the output was changed to $11$11, what would the new input of this function machine be?