1. 5
6
7
8
9
1
2
3
4
5





The Rule is ‘ADD 4’

2. Ahmed
Peter
Ali
Jaweria
Hamad
Paris
London
Dubai
New York
Cyprus




Has Visited
There are MANY arrows from each person and each place is related to MANY
People. It is a MANY to MANY relation.

3. Bilal
Peter
Salma
Alaa
George
Aziz
62
64
66
Person Has A Mass of Kg






In this case each person has only one mass, yet several people have the same
Mass. This is a MANY to ONE relationship

4. Is the length of
14
30
Pen
Pencil
Ruler
Needle
Stick
cm object




Here one amount is the length of many objects.
This is a ONE to MANY relationship

5. FUNCTIONS
• Many to One Relationship
• One to One Relationship

6. Domain Co-domain
0
1
2
3
4
1
2
3
4
5
6
7
8
9
Image Set (Range)
x2x+1
A B

7. f : x  x2
+4
f(x)=x2
+4
The upper function is read as follows:-
‘Function f such that x is mapped onto x2
+4

8. Lets look at some function
Type questions
If
f(x) = x2 + 4 and g(x) = 1 − x2
Find f(2)
Find g(3)
f(x) = x2
+ 42 2 = 8 g(x) = 1 − x2
3 3
= -8

9. Consider the function f(x) = 3x − 1 We can consider this as two simpler
functions illustrated as a flow diagram
Multiply by 3 Subtract 1
3x 3x − 1x
Consider the function f : x  (2x + 5)2
x
Multiply by 2 Add 5
2x 2x + 5
Square
(2x + 5)2

10. f : x  3x + 2 and g(x) : x  x2
Consider 2 functions
fg is a composite function, where g is performed first and then f is performed
on the result of g.
The function fg may be found using a flow diagram
x
square
x2
Multiply by 3
3x2
Add 2
3x2
+ 2
g f
Thus fg = 3x2
+ 2

11. g f
fg(x)
x2
3x + 2
3x2
+ 2
2
4 14
2

12. Consider the function f(x) = 5x − 2
3
Here is its flow diagram
x
x5
x5 -2 f(x) = 5x − 2
3
Draw a new flow diagram in reverse!. Start from the right and go left…
Multiply by 5 Subtract 2 Divide by three
Multiply by threeAdd twoDivide by 5
x3x3x +23x +2
5
f−1
(x) = 3x + 2
5
And so

13. (a)
(b)
(c) (d)
(a) and (c)

14. (a)
(b)
(c) (d)
(a) and (c)

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