Cambridge International Mathematics

386 Introduction to functions (Chapter 19)

Consider these examples:

² All values ofxandyare possible.

) the domain is fxjx 2 Rg

and the range is fyjy 2 Rg.

² All values of x< 2 are possible.

) the domain is fxjx< 2 ,x 2 Rg.

All values of y>¡ 1 are possible.

) the range isfyjy>¡ 1 ,y 2 Rg.

² xcan take any value.

) the domain is fxjx 2 Rg.

ycannot be<¡ 2.

) the range isfyjy>¡ 2 ,y 2 Rg.

² xcan take all values exceptx=0:

) the domain is fxjx 6 =0,x 2 Rg.

ycan take all values excepty=0:

) the range isfyjy 6 =0, y 2 Rg.

Example 2 Self Tutor

For each of the following graphs, state the domain and range:

abc

a Domain:

fxjx 2 Rg.

Range:

fyjy 64 ,y 2 Rg.

b Domain:

fxjx>¡ 4 ,x 2 Rg.

Range:

fyjy>¡ 4 ,y 2 Rg.

c Domain:

fxj¡ 16 x< 4 ,x 2 Rg.

Range:

fyj¡ 26 y< 3 ,y 2 Rg.

It is common practice when dealing with graphs on the Cartesian plane to assume the domain and range are

real. So, it is common to write fxjx 63 , x 2 Rg as just fxjx 63 g.

EXERCISE 19B.1

1 State the domain and range for these sets of points:

a f(¡ 1 ,5),(¡ 2 ,3),(0,4),(¡ 3 ,8),(6,¡1),(¡ 2 ,3)g

b f(5,4),(¡ 3 ,4),(4,3),(2,4),(¡ 1 ,3),(0,3),(7,4)g.

y

x

()2 -1,

O

y

x

()3 ¡4,

O

y

x

()4 -4,

()-4 -2,

O

y

x

-2

-2 2

y= 21 x^2 - 2

O

Rrepresents the set

of all real numbers,

or all numbers on the

number line.

y

x

O

y

O x

()4 ¡3,

()-1 -2,

y

O x

x

y=^3

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Y:\HAESE\IGCSE01\IG01_19\386IGCSE01_19.CDR Tuesday, 7 October 2008 2:39:12 PM PETER