Cambridge International Mathematics

384 Introduction to functions (Chapter 19)

Amappingis used to map the members orelementsof one set called thedomain, onto the members

of another set called therange.

In particular we can define:

² Thedomainof a mapping is the set of elements which are to be mapped.

² Therangeof a mapping is the set of elements which are the result of mapping the elements of the

domain.

Consider these two mappings:

For the mapping y=x+3:

x(domain) y(range)

For the mapping y=x^2 +1:

x(domain) y(range)

y=x+3 or ‘add 3 ontox’ is called aone-onemapping because every element in the domain maps onto

one and only one element in the range.

y=x^2 +1 or ‘squarexand then add 1 ’ is called amany-onemapping because more than one element in

the domain maps onto the same element in the range.

EXERCISE 19A

1 Copy and complete the following ‘sets and mappings’ diagrams, and state whether the mapping is

one-one, many-one, one-many or many-many.

a mapping ‘y=2x¡ 5 ’ b mapping ‘is not equal to’ c mapping ‘x=y^2 ’

d mapping ‘is greater than’ e mapping ‘add 1 ’

2 For these domains and mappings, describe the corresponding range:

a domain freal numbersg mapping: ‘subtract 20 ’

b domain fodd numbersg mapping: ‘double’

c domain fpositive real numbersg mapping: ‘find the square root’

d domain freal numbers> 0 g mapping: ‘add 10 ’

e domain feven numbersg mapping: ‘divide by 2 ’

xy

0

1

2

3

0 1 2 3 0 1 2 3

0

1

2

3

¡ 2

0

7

xy

xy

0

1

4

:

:

:

x :

y

:

¡ 2

0

6

¡ 11

1

3

9

¡ 8

¡ 1

0

1

2

2

1

5

-2 -1 0 1 2 3 4 5 6 7

-2 -1 0 1 2 3 4 5 6 7

In the example of “is a child of ”, the mapping ismany-many.

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Y:\HAESE\IGCSE01\IG01_19\384IGCSE01_19.CDR Tuesday, 21 October 2008 1:59:23 PM PETER