Cambridge International Mathematics

Introduction to functions (Chapter 19) 395

EXERCISE 19E

1 Consider the function y=

5

x

, which can be written as xy=5:

a Explain why bothxandycan take all real values except 0 :

b What are the asymptotes of the function y=

5

x

?

c Findywhen: i x= 500 ii x=¡ 500

d Findxwhen: i y= 500 ii y=¡ 500

e By plotting points or by using technology, graph y=

5

x

.

f Without calculating new values, sketch the graph of y=

¡ 5

x

.

2 Kate has to make 40 invitations for her birthday party. How fast she can make the invitations will affect

how long the job takes her.

Suppose Kate can makeninvitations per hour and the job takes herthours.

Invitations per hour (n) 4 8 12 ....

Time taken (t)

a

b Draw a graph ofnversustwithnon

the horizontal axis.

c Is it reasonable to draw a smooth curve through the points plotted inb? What shape is the curve?

d State a formula for the relationship betweennandt.

3 Determine the equations of the following reciprocal graphs:

abc

4 For the following functions:

i use technology to graph the function

ii find the equation of any vertical or horizontal asymptotes.

a y=

3

x¡ 2

b y=

2

x+1

c y=

1

x¡ 3

+1

Discovery 3 The absolute value function

#endboxedheading

What to do:

1 Suppose y=x if x> 0 and y=¡x if x< 0.

Findyfor x=5, 7 ,^12 , 0 ,¡ 2 ,¡ 8 , and¡ 10 :

F THE ABSOLUTE VALUE FUNCTION [1.6, 3.2]

Instructions for

graphing a function

can be found on

page 22.

y

x

()4 ¡2,

O

y

x

()-3 -1,

O

y

x

()2 -6,

O

Complete a table of values:

IGCSE01

cyan magenta yellow black

(^05255075950525507595)
100 100
(^05255075950525507595)
100 100
y:\HAESE\IGCSE01\IG01_19\395IGCSE01_19.CDR Friday, 10 October 2008 10:17:37 AM PETER