Page 27 - MAT KS3 Y8 Cambridge CheckPoint

2.4 Using functions and mappings

✦ Exercise 2.4

1 a Copy and complete the table of values for each function machine.

i x + 3 y ii x – 3 y

x 1 2 3 4 x 4 5 6 7

y y
b Draw a mapping diagram for each function in part a.
c Write each function in part a as an equation.
2 a Copy and complete the table of values for each function machine.
i ii
x × 2 + 3 y x × 3 – 1 y When you are given a
y-value and need to work
x 1 2 4 x 3 5 12 out the x-value you must
work backwards through
y 15 y 26 the function machine.
For example, in part 2(a)
iii iv
x ÷ 2 + 5 y x ÷ 2 – 3 y (i) we are given y = 15 and
a function machine that
x 4 10 x 2 8 tells us to multiply x by 2,
then add 3. So, working
y 9 15 y −1 4
backwards we would
b Write each function in part a as an equation. subtract 3 from 15 to give
12. Then divide 12 by 2.
3 a Work out the rule for each function machine.
x y x y
i ii
2 10 3 15
6 ... 14 5 ... 25
10 18 8 40
b Write each function in part a as an equation.

4 Mia and Razi are looking at this function machine.
x y
4 13
6 ... ... 21
9 33

I think the equation for this I think the equation for this
function is y = 3x + 1. function is y = 4x – 3.

Which of them is correct? Explain your answer.
5 Work out the equation for this function machine.
x y

1 5
2 ... ... 8
3 11
Explain how you worked out your answer.
2 Sequences, expressions and formulae 25