functions
TRANSCRIPT
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)
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