Cambridge International Mathematics

Introduction to functions (Chapter 19) 397

EXERCISE 19F.1

1 Write down the values of:

a j 7 j b j¡ 7 j c j 0 : 93 j d

̄

̄¡ 21

4

̄

̄ e j¡ 0 : 0932 j

2 Ifx=¡ 4 , find the value of:

a jx+6j b jx¡ 6 j c j 2 x+3j d j 7 ¡xj

e jx¡ 7 j f

̄

̄x^2 ¡ 6 x

̄

̄ g

̄

̄ 6 x¡x^2

̄

̄ h jxj

x+2

3aFind the value ofa^2 andjaj^2 ifais:

i 3 ii 0 iii ¡ 2 iv 9 v ¡ 9 vi ¡ 20

b What do you conclude from the results ina?

4 Solve forx:

a jxj=4 b jxj=1: 4 c jxj=¡ 2 d jxj+1=7

e jx+1j=3 f j 2 ¡xj=5 g 5 ¡jxj=1 h j 5 ¡xj=1

a b jabj jajjbj

̄

̄

̄

a

b

̄

̄

̄

jaj

jbj

12 3

12 ¡ 3

¡ 12 3

¡ 12 ¡ 3

5aCopy and complete:

b What can you conclude from the results ina?

6 By replacingjxjwithxfor x> 0 and(¡x)for x< 0 , write the following functions without the

modulus sign and hence graph each function:

a y=¡jxj b y=jxj+x c y=

jxj

x

d y=x¡ 2 jxj

a b ja+bj jaj+jbj ja¡bj jaj¡jbj

2 5

2 ¡ 5

¡ 2 5

¡ 2 ¡ 5

7aCopy and complete:

b What can you conclude from the results

ina?

Example 8 Self Tutor

Draw the graph of f(x)=x+2jxj:

If x> 0 ,

f(x)=x+2(x)=3x

If x< 0 ,

f(x)=x+2(¡x)=¡x

y

x

yx¡=¡-

yx¡=¡3

O

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y:\HAESE\IGCSE01\IG01_19\397IGCSE01_19.CDR Friday, 10 October 2008 10:20:45 AM PETER