Page 25 - Mathematics Coursebook

2.3 Representing simple functions

2.3 Representing simple functions

A function is a relationship between two sets of numbers.
A function can be shown as a function machine like this.
This function machine adds 3 to any
2 5 number that goes into the machine.
4 + 3 7
5 8

"e numbers that you put into the function machine are called the input.
"e numbers that you get out of the function machine are called the output.

A function can also be shown as a mapping diagram like this.

Input 01 2345678 910
We say that 2 maps to 5,
4 maps to 7 and
5 maps to 8.
Output 0 1 2345678 910

Worked example 2.3

a Find the missing inputs and outputs in this function machine.
Input Output
1 ...
3 × 2 ...
... 10
b Draw a mapping diagram to show the function in part a.

a Input Output To work out the outputs, multiply the inputs by 2.
1 × 2 = 2, 3 × 2 = 6
1 × 2 2 To work out the input, work backwards and divide the
3
6
5 10 output by 2.
10 ÷ 2 = 5
b Input 01 2345678 910
1 maps to 2, 3 maps to 6
and 5 maps to 10.
Output 0 1 2345678 910

) Exercise 2.3

1 Copy these function machines and work out the missing inputs and outputs.
a Input Output b Input Output c Input Output d Input Output
2 ... 7 ... 4 ... 8 ...
5 + 7 ... ... – 5 5 5 × 3 ... ... ÷ 2 6
... 16 15 ... ... 30 ... 9

24 2 Sequences, expressions and formulae