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

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One to One

1

2

3

4

5

5

6

7

8

9

The Rule is ‘ADD 4’


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.


Person Has A Mass of Kg

Bilal

Peter

Salma

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 ONErelationship


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


FUNCTIONS

  • Many to One Relationship

  • One to One Relationship


Function - Domain and Range!

x2x+1

A

B

0

1

2

3

4

1

2

3

4

5

6

7

8

9

Image Set (Range)

DomainCo-domain


Functions - Notation

The upper function is read as follows:-

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


Lets look at some function

Type questions

(

)

=

+

(

)

=

-

2

2

f

x

x

4

a

n

d

g

x

1

x

(

)

F

i

n

d

f

2

(

)

F

i

n

d

g

3

If

= 8

= -8

2

2

3

3


Flow Diagrams

We can consider this as two simpler

functions illustrated as a flow diagram

Multiply by 3

Subtract 1

Square

Multiply by 2

Add 5


Thus

=

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

Add 2

square

Multiply by 3


Composite Functions - Arrow Diagram

2

14

4

2


Consider the function

Here is its flow diagram

-2

5

5

Divide by three

Subtract 2

Multiply by 5

3

3

3

+2

+2

5

Divide by 5

Multiply by three

Add two

And so

Inverse Functions

Draw a new flow diagram in reverse!. Start from the right and go left…


Which Are Functions?

(b)

(a)

(d)

(c)

(a) and (c)


Which Are Functions?

(b)

(a)

(d)

(c)

(a) and (c)


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