Cambridge International Mathematics

396 Introduction to functions (Chapter 19)

2 Draw the graph of y=

(

x if x> 0

¡x if x< 0

using the results of 1.

3 Consider M(x)=

p

x^2 wherex^2 must be found before finding the square root.

Find the values of M(5),M(7),M(^12 ),M(0),M(¡ 2 ),M(¡8)andM(¡10).

4 What conclusions can be made from 1 and 3?

THE ABSOLUTE VALUE OF A NUMBER

Theabsolute valueormodulusof a real number is its size, ignoring its sign.

We denote the absolute value ofxbyjxj.

For example, the absolute value of 7 is 7 , and

the absolute value of¡ 7 is also 7.

Geometric definition of absolute value

If x> 0 :Ifx< 0 :

For example:

Algebraic definition of absolute value

FromDiscovery 3,

The vertical line

x=0is the

line of symmetry

of the graph.

Example 7 Self Tutor

a ja+bj

=j¡7+3j

=j¡ 4 j

=4

b jabj

=j¡ 7 £ 3 j

=j¡ 21 j

=21

The absolute value

behaves as a grouping

symbol. Perform all

operations within it first.

77

-7 07

||x

0 x

||x

x 0

y

x

This branch

isyxx= -, <0.

This branch

isyxx= , >0.

O

jxjis the distance ofxfrom 0 on the number line.

Because the modulus is a distance, it cannot be negative.

jxj=

(

x ifx> 0

¡x ifx< 0

or jxj=

p

x^2

y=jxj has graph:

If a=¡ 7 and b=3find: a ja+bj b jabj

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y:\HAESE\IGCSE01\IG01_19\396IGCSE01_19.cdr Friday, 10 October 2008 10:17:52 AM PETER