Page 26 - Mathematics Coursebook

2.3 Representing simple functions

2 Copy these function machines and work out the missing inputs and outputs.
Input Output Input Output
Input
Output
Input
Output
Input
a Input Output b Input Output
Output
Output
Input
2 2 5 5 4 4 ... ...
... ...
5 5
5 2 2 5 × 2 × 2 + 1 + 1 ... ... 6 4 4 6 ÷ 2 ÷ 2 + 5 + 5 ... ...
... ...
... 5 5 × 2 × 2 + 1 + 1 9 ... ... 10 6 6 ÷ 2 ÷ 2 + 5 + 5 ... ...
9
10
...
... ... 9 9 1010 ... ...
c Input Output d Input Output
Input
Input
Output
Output
Input
Input
Output
Input Output Input Output
Output
1 1 ... ... 6 6 ... ...
... ...
6 6
... ...
3 1 1 3 + 7 + 7 × 2 × 2 ... ... ... ... – 4 – 4 × 3 × 3 12 12
... ...
1212
... ...
... 3 3 + 7 + 7 × 2 × 2 24 24 ... ... – 4 – 4 × 3 × 3 24 24
...
... ... 2424 ... ... 2424
3 a Work out the rule to complete each of these function machines.
i Inputt Output ii Inputt Outputt
Outpu
Inpu
Output
Inpu
1 1 5 5 8 8 4 4
3 3 ... ... 7 7 6 6 ... ... 3 3
5 5 9 9 2 2 1 1
b Make two copies of the diagram below.
Input 01 2345678 910
Output 0 1 2345678 910
Draw a mapping diagram for each of the functions in part a.
4 Tanesha and Dakarai look at this function machine.
Test the input numbers in each of their
Input Output functions to see if either of them is correct.
2 2
5 ... ... 14
8 26
I think the function is: ‘Multiply by 4
I think the function is: ‘Multiply
then take away 6.’
by 3 then take away 4.’
Is either of them correct? Explain your answer.

5 Chin-Mae draws this mapping diagram and function machine for the same function.

01
23456789 10
Input
Input 01 23456789 10
Input Input Output Output
... ... ... ...
... ... ... ... ... ... ... ...
... ... ... ...
23456789 10
Output 0 1 Output 0 1 23456789 10

Fill in the missing numbers and the rule in the function machine.
2 Sequences, expressions and formulae 25