Cambridge Additional Mathematics

GRAPHING

PACKAGE

Surds, indices, and exponentials (Chapter 4) 121

EXERCISE 4G

1 Use the graph of y=2x to estimate the value of:

a 2

1

(^2) or
p
2 b 20 :^8 c 21 :^5 d 2 ¡
p
2
2
a 2 x=3 b 2 x=0: 6 c 2 x=4: 3 d 2 x=0: 3
3 Use the graph of y=2x to explain why 2 x=0 has no solutions.
4 Suppose f(x)=2£ 3 x. Find:
a f(0) b f(3) c f(¡2)
5 Suppose g(x)=5x+2.
ab
6 Draw freehand sketches of the following pairs of graphs using your observations from
the previousDiscovery:
a y=2x and y=2x¡ 2 b y=2x and y=2¡x
c y=2x and y=2x¡^2 d y=2x and y= 2(2x)
7 Draw freehand sketches of the following pairs of graphs:
a y=3x and y=3¡x b y=3x and y=3x+1
c y=3x and y=¡ 3 x d y=3x and y=3x¡^1
8 For each of the functions below:
i Sketch the graph of the function.
ii State the domain and range.
iii Use your calculator to find the value ofywhen x=
p
2.
iv Discuss the behaviour ofyas x!§1.
v Determine the horizontal asymptotes.
a y=2x+1 b f(x)=2¡ 2 x c y=2¡x+3 d f(x)=3¡ 2 ¡x

Example 26 Self Tutor

An entomologist monitoring a grasshopper plague notices

that the area affected by the grasshoppers is given by

A(n) = 1000£ 20 :^2 n hectares, wherenis the number

of weeks after the initial observation.

a Find the original affected area.

b Find the affected area after:

i 5 weeks ii 10 weeks iii 12 weeks.

c Draw the graph ofAagainstn.

d How long will it take for the affected area to reach 8000 hectares?

a A(0) = 1000£ 20

= 1000£ 1

= 1000 ) the original affected area was 1000 ha.

Use the graph of y=2x to estimate the solution to:

Find g(0) and g(¡1). Findasuch that g(a)=27.

4037 Cambridge

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Y:\HAESE\CAM4037\CamAdd_04\121CamAdd_04.cdr Tuesday, 14 January 2014 2:29:10 PM BRIAN