Cambridge International Mathematics

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-3 x

3

O

y

x

O 3

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GRAPHING

PACKAGE

4aExplain why the horizontal line test is a valid test for the existence of an inverse function.

b Which of the following functions have an inverse function?

i ii iii iv

5 Show that these functions do not have an inverse function:

a f(x)=x^2 b f(x)=

1

x^2

c f(x)=x^2 +4x+4

6aOn the same set of axes graph y=f(x) and y=f¡^1 (x) for:

i f(x)=2x+1 ii f(x)=

2

x

iii f(x)=

p

x, x> 0

b Copy and complete:

The graph of y=f¡^1 (x) is a reflection of y=f(x) in ..........

7 If f(x) has a vertical asymptote of x=k, explain why f¡^1 (x) will have a horizontal asymptote

y=k.

8 For the following functions:

i find f¡^1 (x) ii graph f(x) and f¡^1 (x) on a set of axes.

a f(x)=

2

x¡ 3

b f(x)=¡

3

x+1

c f(x)=

x

x¡ 2

d f(x)=

x+1

x¡ 1

e f(x)=

1

x^3 ¡ 1

f f(x)=

2 x+1

x¡ 3

What do you notice about the graphs of y=f(x) and y=f¡^1 (x) in each case?

A graphics calculator or computer graphing package are useful tools for gaining knowledge about a function,

in particular one with an unfamiliar form.

We can use a graphics calculator to obtain:

² a table of values for a function

² a sketch of the function

² thezerosorx-interceptsof the function

² they-intercept of the function

² any asymptotes of the function

² the turning points of the function where it is alocal maximumorlocal minimum

² the points of intersection of two functions.

Instructions for using your calculator are found beginning on page 22.

C USING TECHNOLOGY [2.11, 3.6]

Further functions (Chapter 23) 475

IGCSE01

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Y:\HAESE\IGCSE01\IG01_23\475IGCSE01_23.CDR Monday, 27 October 2008 2:18:42 PM PETER