Cambridge Additional Mathematics

54 Functions (Chapter 2)

2 Draw sign diagrams for:

a (x+ 4)(x¡2) b x(x¡3) c x(x+2)

d ¡(x+ 1)(x¡3) e (2x¡1)(3¡x) f (5¡x)(1¡ 2 x)

g (x+2)^2 h 2(x¡3)^2 i ¡3(x+4)^2

Example 16 Self Tutor

Draw a sign diagram for

x¡ 1

2 x+1

.

x¡ 1

2 x+1

is zero when x=1and undefined when x=¡^12.

When x=10,

x¡ 1

2 x+1

=

9

21

> 0

Since (x¡1) and (2x+1)are single factors, the signs alternate.

3 Draw sign diagrams for:

a

x+2

x¡ 1

b

x

x+3

c

2 x+3

4 ¡x

d

4 x¡ 1

2 ¡x

e

3 x

x¡ 2

f

¡ 8 x

3 ¡x

g

(x¡1)^2

x

h

4 x

(x+1)^2

i

(x+ 2)(x¡1)

3 ¡x

j

x(x¡1)

2 ¡x

k

(x+ 2)(x¡2)

¡x

l

3 ¡x

(2x+ 3)(x¡2)

4 Draw sign diagrams for:

a 1+^3

x+1

b x¡^1

x

c x¡^1

x^2

The operations of+and¡,£and¥, areinverse operationsas one undoes what the other does.

For example, x+3¡3=x and x£ 3 ¥3=x.

The function y=2x+3 can be “undone” by itsinverse function y=

x¡ 3

2

We can think of this as two machines. If the machines are inverses then the second machineundoeswhat

the first machine does.

No matter what value ofxenters the first machine, it is returned as the output from the second machine.

G Inverse functions

• \Qw^1

+-+

x

• \Qw^1

+

x

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Additional Mathematics
Y:\HAESE\CAM4037\CamAdd_02\054CamAdd_02.cdr Thursday, 3 April 2014 4:09:09 PM BRIAN