5 6

7

8

9

1

2

3

4

5

The Rule is ‘ADD 4’

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 MANYPeople. It is a MANY to MANY relation.

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

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

FUNCTIONS

• Many to One Relationship

• One to One Relationship

Domain Co-domain

0

1

2

3

4

123456789

Image Set (Range)

x2x+1A B

f : x x2 4

fxx2 4

The upper function is read as follows:-

‘Function f such that x is mapped onto x2+4

Lets look at some functionType questions

If fx x 2 4 and gx 1 x 2

Find f2

Find g3

fx x2 42 2 = 8 gx 1 x2

3 3

= -8

Consider the function fx 3x 1 We can consider this as two simpler functions illustrated as a flow diagram

Multiply by 3 Subtract 13x 3x 1x

Consider the function f : x 2x 52

xMultiply by 2 Add 5

2x 2x 5Square

2x 52

f : x 3x 2 and gx : x x2Consider 2 functions

fg is a composite function, where g is performed first and then f is performedon the result of g.The function fg may be found using a flow diagram

xsquare

x2

Multiply by 33x2

Add 23x2 2

g f

Thus fg = 3x2 2

g f

fg x

x2 3x 2

3x2 2

24 14

2

Consider the function fx 5x 23

Here is its flow diagram

xx5

x5 -2 fx 5x 23

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

x3 x3 x +23 x +25

f 1x 3x 25And so

(a)

(b)

(c) (d)

(a) and (c)

(a)

(b)

(c) (d)

(a) and (c)