Cambridge International Mathematics

x ¡ 3 ¡ 2 ¡ 1 0 1 2 3

y

4aComplete the table of values shown for the function

f(x)=3x.

b Use the table of values inato graph y=f(x):

c On the same set of axes and without a table of values, graph:

i y=¡f(x) ii y=f(¡x) iii y=2f(x) iv y=f(2x):

5aClick on the icon to obtain a printable graph of y=2x.

Use the graph to estimate, to one decimal place, the value of:

i 20 :^7 ii 21 :^8 iii 2 ¡^0 :^5 :

b Check your estimates inausing the ^ key on your calculator.

c Use the graph to estimate, correct to one decimal place, the solution of the equation:

i 2 x=5 ii 2 x=1: 5 iii 2 x=¡ 1 :

6

7 For the following functions:

i sketch the graph ii find they-intercept iii find the equation of any asymptote.

a f(x)=(1:2)x b f(x)=2x¡ 1 c f(x)=2x¡^1 d f(x)=2x+1

e f(x)=3+2x f f(x)=2¡ 2 x g f(x)=

2 ¡x+1

3

h f(x) = 2(3¡x)+1

8 Explain why (¡2)x is undefined for some real numbersx.

9 Find the exponential function corresponding to the graph:

ab

Anexponential equationis an equation in which the unknown occurs as part of the exponent or index.

For example: 2 x=8 and 30 £ 3 x=7 are both exponential equations.

If 2 x=8, then 2 x=2^3. Thus x=3 is a solution, and it is in fact the only solution.

C EXPONENTIAL EQUATIONS [2.11]

Graph ofy=2x

P

t

400

()2 ¡16,

O

M

x

()3 ¡8,

()1 ¡72,

O

Find the image of:

a y=2x under the translation

¡¡ 1

3

¢

b y=3x under the translation

¡ 2

¡ 4

¢

c y=2¡x under:

i a reflection in thex-axis ii a reflection in they-axis iii a reflection in the line y=x

d y=3x under:

i a stretch with invariantx-axis and scale factor 2

ii a stretch with invarianty-axis and scale factor^13.

570 Exponential functions and equations (Chapter 28)

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Y:\HAESE\IGCSE01\IG01_28\570IGCSE01_28.CDR Tuesday, 28 October 2008 12:48:00 PM PETER