Cambridge International Mathematics

5 For these functions:

i Use your graphics calculator to obtain a sketch of the function.

ii State the equations of any asymptotes.

iii Find the axes intercepts.

iv Find and classify any turning points.

a f(x)=

4

x¡ 2

b f(x)=2¡

3

x+1

c f(x)=2x¡ 3

d f(x)=2x+

1

x

e f(x)=

4 x

x^2 ¡ 4 x¡ 5

f f(x)=3¡x+2

g f(x)=

x^2 ¡ 1

x^2 +1

h f(x)=

x^2 +1

x^2 ¡ 1

i f(x)=

2 x+3

2 x+1

6 Consider f(x)=2x¡x^2

a Find the values of f(x) for x=¡ 2 ,¡ 1 , 0 , 1 , 2 , 3 , 4 , 5.

b Useato set a suitable window on your graphics calculator

and hence obtain a sketch graph for f(x) on ¡ 26 x 65.

c Find the zeros of f(x).

d Find the turning points of f(x).

x f(x) g(x) h(x)

¡ 2

¡ 1 : 5

¡ 0 : 5

0

0 : 5

1

2

2 : 7

3 : 61

7 If f(x)=2x, g(x)=x^2 ¡ 1 and h(x)=

x¡ 1

2 x+1

,

copy and complete, giving answers correct to 3 decimal places

where necessary.

8aUse your graphics calculator to draw, on the same axes,

the functions f(x)=x¡

1

x

and g(x)=2¡x¡ 1.

b State the equations of the asymptotes of f(x).

c Find the coordinates of any points where y=f(x) and y=g(x) meet.

9 Consider f(x)=

x^2 +4

x^2 +1

:

a Sketch the graph of y=f(x).

b Find the domain and range of f(x).

c Write down the equations of any asymptotes of y=f(x).

d Find the coordinates of any points where y=f(x) meets y=5.

e Suppose y=f(x) meets y=k at exactly two points.

What possible values couldkhave?

Did you notice in

that vertical

asymptotes can be

found by letting the

denominator be? 0

5

Further functions (Chapter 23) 477

IGCSE01

cyan magenta yellow black

(^05255075950525507595)
100 100
(^05255075950525507595)
100 100
Y:\HAESE\IGCSE01\IG01_23\477IGCSE01_23.CDR Monday, 27 October 2008 2:18:48 PM PETER