5 67895 6789 1234512345 the rule is add 4 ahmed peter ali jaweria hamad paris london dubai new york...
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5 6
7
8
9
1
2
3
4
5
The Rule is ‘ADD 4’
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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.
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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
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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
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FUNCTIONS
• Many to One Relationship
• One to One Relationship
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Domain Co-domain
0
1
2
3
4
123456789
Image Set (Range)
x2x+1A B
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f : x x2 4
fxx2 4
The upper function is read as follows:-
‘Function f such that x is mapped onto x2+4
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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
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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
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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
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g f
fg x
x2 3x 2
3x2 2
24 14
2
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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
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(a)
(b)
(c) (d)
(a) and (c)
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(a)
(b)
(c) (d)
(a) and (c)