Cambridge International Mathematics

(Tina Sui) #1
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

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