Transcript 1     5  The Rule is ‘ADD 4’ 7 Ahmed  Paris Peter  London Ali Dubai Jaweria  New York Cyprus Hamad  Has Visited There are MANY arrows from each person and.

1 
5
2

3

4

8
5 
9
The Rule is ‘ADD 4’
6
7
Ahmed 
Paris
Peter 
London
Ali
Dubai
Jaweria

New York
Cyprus
Hamad 
Has Visited
There are MANY arrows from each person and each place is related to MANY
People. It is a MANY to MANY relation.
Person
Bilal
Has A Mass of


Salma 
Kg
62
Peter
Alaa

George 
Aziz
64
66

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
cm

14 
object
Pen
Pencil
Ruler

30 
Needle
Stick
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
x2x+1
A
B
0
1
2
3
4
Domain
1
2
3
4
5
6
7
8
9
Co-domain
Image Set (Range)
f : x x 2  4
fx  x 2  4
The upper function is read as follows:‘Function f such that x is mapped onto x2+4
Lets look at some function
Type questions
If
f  x   x 2  4 and g  x   1 - x 2
F ind f  2 
F ind g  3 
fx
4
2
2  x
2
=8
gx  1 - x 2
3
3
= -8
Consider the function fx  3x - 1
x
We can consider this as two simpler
functions illustrated as a flow diagram
3x
Multiply by 3
Subtract 1
3x - 1
Consider the function f : x 2x  5 2
x
Multiply by 2
2x
Add 5
2x  5
Square
2x  5 2
Consider 2 functions
f : x 3x  2 and gx : x x 2
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
g
Thus f g
= 3x 2  2
x2
Multiply by 3
3x 2
f
Add 2
3x 2  2
3x  2
x2
f
g
2
4
2
f g x
3x 2  2
14
Consider the function
fx  5x - 2
3
Here is its flow diagram
5 x -2
5x
x
Multiply by 5
Subtract 2
fx  5x - 2
3
Divide by three
Draw a new flow diagram in reverse!. Start from the right and go left…
3 x +2
5
3x
3 x +2
Divide by 5
And so
f -1 x  3x  2
5
Add two
x
Multiply by three
(b)
(a)
(c)
(d)
(a) and (c)
(b)
(a)
(c)
(d)
(a) and (c)
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