Scribd
Upload
103 views8 pages

Function

The document contains 10 problems related to functions and relations. The problems involve identifying the domain, codomain, range and type of relations based on arrow diagrams, graphs or ordered pairs. They also involve determining images, inverses and evaluating functions. The problems require classifying relations as one-to-one, many-to-one or onto, completing partial functions and finding constants in given functions.

Uploaded by

nurza83
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as DOC, PDF, TXT or read online on Scribd
103 views8 pages

Function

The document contains 10 problems related to functions and relations. The problems involve identifying the domain, codomain, range and type of relations based on arrow diagrams, graphs or ordered pairs. They also involve determining images, inverses and evaluating functions. The problems require classifying relations as one-to-one, many-to-one or onto, completing partial functions and finding constants in given functions.

Uploaded by

nurza83
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as DOC, PDF, TXT or read online on Scribd
You are on page 1/ 8

1.

FUNCTIONS:
Express the relation between the following pairs of sets in the form of arrow diagram,
ordered pair and graph.
Arrow diagram
Ordered pair
Graph

a ) Set A =
Kelantan, Perak ,
Selangor
Set B = Shah Alam ,
Kota Bharu ,Ipoh
Relation: City of the
state in Malaysia
b )Set A =
triangle,rectangle,
pentagon
Set B = 3,4,5
Relation : Number of
Sides

Determine domain , codomain , object, image and range of relation.


1. Diagram 1 shows the relation between set P and set Q.

3
2

-2

-3

Set P

a.
b.
c.
d.
e.
f.

Diagram 1

Set Q

Domain =

Codomain =
Object
=
Image
=
Range
=...
Ordered Pairs =

Classifying the types of relations

State the type of the following relations


a)

x
2

..
c)

3
2
-3

-2
-3

36

16

xX

b)

X2

4
9

..

.
Type of number

d)
4
9
-3

Prime
Even

1. Diagram 1 shows the relations between two sets of number.

9
DIAGRAM 1

(a) State the type of relation between set A and set B.


(b) Using function notation, write a relation between set A and set B.
[ 2 marks ]

Answer(a)____________
_____
(b) _________________
2. Given the function h such that h( x) x 2 kx 5 . Find the value of k given

h(3) 2

[2 marks]

Answer : _________________

3.

The ordered pairs of a certain relation are given as


{ ( 0, 0 ), ( 1, 1 ), ( 2, 4 ), ( 3, 9 ) }. Identify
(a) the domain
(b) the range
of the relation.

[2 marks]

Answer :
(a)____________
(b)____________
4.

Diagram 2 shows the graph of a quadratic function


f(x) = x2.
y
y=f(x)

State

DIAGRAM 2

(a) the type of relation


(b) whether the graph indicates a function.

[ 2 marks ]

Answer :
(a) ________
(b) ________

5. In Diagram 3, set Q shows the images of certain elements of set P


2
1

-1

-2
Set Q

Set P
DIAGRAM 3

(a) State the type of relation between set P and set Q


(b) Using the function notation, write a relation between set P and set Q
[2 marks]

Answer (a)__________________
(b) _________________

m 9x
x

1
3

27
DIAGRAM 4

1
6. Diagram 4 shows the function f : x

Find the value of

m 9x
, x 0 , where m is a constant.
x

[2 marks]

Answer:____________________

7.
1
2
3

4
5
6

1
2
3

4
5
6

1
2
3

4
5
6

The arrow diagrams above represents three different relations.


( a ) Which one represents the function?
( b ) Write down the range of the function.
[ 2 marks ]
Answer: ( a )
( b )

8. The arrow diagram shows part of the function

f : x x 2 2, complete the diagram below.


[ 2 marks ]

Answer:
x

f ( x)

-1

-1

-2

9.

Diagram 5 shows the mapping of x onto y by the function f.

6
7
8

3
4
5
DIAGRAM 5

Determine
(a) f(6)
(b) f 1 (5)
(2 marks)
Answer :(a)____________
(b)____________
10.

Diagram 6 shows the function g : x

mx
,
2
mx
2

x
g

DIAGRAM 6

Find the value of m


Answer :____________

Answer SET 1

1.

(a) one to one (b) f : x 3 x

2.

k= -4

a) { 0, 1, 2,3 }
b) { 0, 1, 4, 9 }

4.

a) Many to one
b) Yes

5.

6.

(a) many to one


(b) f ( x) x 2 2

m 12

7.

a) B

8.

b) {4,5}
x

9.

10.

f(x)

-1

-1

-2

(a) 3 , (b) 8

m = 10

You might also like