Cambridge International Mathematics

Introduction to functions (Chapter 19) 385

We can also use set notation to describe mappings.

For example, consider the set f 0 ,§ 1 ,§ 2 ,§ 3 g under the mapping ‘square the number’.

f 0 ,§ 1 ,§ 2 ,§ 3 g maps onto f 0 , 1 , 4 , 9 g

We could write this mapping as x 7 !x^2

This is a many-one mapping, and is an example of afunction.

Afunctionis a mapping in which each element of the domain maps ontoexactly oneelement of the range.

is amany-one

mapping and is a

function.

is aone-many

mapping and isnot

a function.

We can see that functions can only be one-one or many-one mappings. One-many and many-many mappings

arenotfunctions.

Example 1 Self Tutor

For the domainf 0 , 1 , 2 , 3 gand the function ‘subtract 2 ’, find the range.

So, the range is f¡ 2 ,¡ 1 , 0 , 1 g

Suppose a function maps setAonto setB. We say that:

² Ais thedomainof the function ² Bis therangeof the function.

To help describe the domain and range of a function, we can use interval notation:

For numbersbetweenaandbwe write a<x<b.

For numbers ‘outside’aandbwe writex<aor x>b:

would be written as a 6 x<b.

A filled in circle indicates the inclusion of the end point.

An open circle indicates the non-inclusion of that point.

B FUNCTIONS [3.1, 3.2]

0

1

2

3

¡ 2

¡ 1

0

1

2

4

6

8

xy

10

1

2

3

0

¡ 1

1

¡ 2

2

¡ 3

3

x

0 1 4 9 y 1 2 3 4

xy

5

0

1

ab

x

ab

x

ab

x

ab

x

We say that: f 0 ,§ 1 ,§ 2 ,§ 3 g is the domain and

f 0 , 1 , 4 , 9 g is the range.

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Y:\HAESE\IGCSE01\IG01_19\385IGCSE01_19.CDR Friday, 14 November 2008 10:43:43 AM PETER