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

2. Paris
London
Dubai
New York
Cyprus
Ahmed
Peter
Ali
Jaweria
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.

3.       Person Has A Mass of Kg Bilal 62 Peter Salma 64 Alaa
George
Aziz 62 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

4. Is the length of cm
object 
Pen
Pencil
Ruler
Needle
Stick  14 30   
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. Function - Domain and Range!
x2x+1 A B 1 2 3 4 1 2 3 4 5 6 7 8 9
Image Set (Range)
Domain Co-domain

7. Functions - Notation 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 f ( x ) = 2 + 4 a n d g 1 - F i 3 If
= 8 2 2
= -8 3 3

9. Flow Diagrams We can consider this as two simpler
functions illustrated as a flow diagram
Multiply by 3
Subtract 1
Multiply by 2
Add 5
Square

10. Compound(Composite) Functions
Consider 2 functions
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
square
Multiply by 3
Add 2
Thus =

11. Composite Functions - Arrow Diagram2 4 14 2

12. Inverse Functions Consider the function Here is its flow diagram 5 -2
Multiply by 5
Subtract 2
Divide by three
Draw a new flow diagram in reverse!. Start from the right and go left… 3 +2 5 3 +2 3
Multiply by three
Add two
Divide by 5
And so

13. Which Are Functions?
(b)
(a)
(c)
(d)
(a) and (c)

14. Which Are Functions?
(b)
(a)
(c)
(d)
(a) and (c)

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