Cambridge International Mathematics

Introduction to functions (Chapter 19) 387

2 For each of the following graphs, find the domain and range and decide whether it is the graph of a

function:

abc

de f

gh i

Incanddwe

assume that

x 2 R.

3 Find the range for the functions with domainD:

a D=f¡ 1 , 0 , 2 , 7 , 9 g, function: ‘add 3 ’.

b D=f¡ 2 ,¡ 1 , 0 , 1 , 2 g, function: ‘square and then divide by 2 ’.

c D=fxj¡ 2 <x< 2 g, function: ‘multiplyxby 2 then add 1 ’.

d D=fxj¡ 36 x 64 g, function: ‘cubex’.

4 For each of these functions:

i use a graphics calculator to help sketch the function

ii find the range.

a y=3x+1 on the domain fxj¡ 26 x 62 g

b y=x^2 on the domain fxj¡ 36 x 64 g

c y=4x¡ 1 on the domain fxj¡ 26 x 63 g

d y=

1

x¡ 1

on the domain fxj 06 x 63 , x 6 =1g

e y=x+

1

x

on the domain fxj¡ 46 x 64 , x 6 =0g

f y=x^2 +1 on the domain fxjx 2 Rg

g y=x^3 on the domain fxjx 2 Rg

GEOMETRIC TEST FOR FUNCTIONS: ‘‘VERTICAL LINE TEST”

If we draw all possible vertical lines on the graph of a relation:

² the relation is a function if each line cuts the graph no more than once

² the relation isnota function ifanyline cuts the graph more than once.

y

O 2 x

y

x

3

-3 3

-3

O

y

x

()-4 -2,

O

y

x

O

y

x

-5

O

y

x

()-2 ¡1,

O

y

x

()6 ¡4,

O

y

x

-5

O

y

1 x

O

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y:\HAESE\IGCSE01\IG01_19\387IGCSE01_19.CDR Friday, 3 October 2008 9:46:45 AM PETER