Cambridge International Mathematics

398 Introduction to functions (Chapter 19)

THE GRAPH OF y=jax+bj

One way of graphing y=jax+bj is to first graph y=ax+b.

Whatever part of the graph is below thex-axis we then reflect in thex-axis.

Example 9 Self Tutor

Graph y=j 2 x¡ 3 j. Comment on any symmetry in the graph.

We begin by graphing y=2x¡ 3.

x 0 1 2

y ¡ 3 ¡ 1 1

The graph cuts thex-axis when y=0.

) 2 x¡3=0

) x=^32

To obtain the graph of y=j 2 x¡ 3 j we

reflect all points withx<^32 in thex-axis.

x=^32 is a vertical line of symmetry.

EXERCISE 19F.2

1 Sketch the graphs of:

a f(x)=jx+1j b f(x)=jx¡ 1 j c f(x)=j 2 x¡ 1 j

d f(x)=j 4 ¡xj e f(x)=j 2 ¡ 3 xj f f(x)= j 3 x+2j

2 What is the equation of the line of symmetry of f(x)=jax+bj?

3 Find the function f(x)=jax+bj which has the graph:

abc

Review set 19A

#endboxedheading

1 For these functions, find the domain and range:

ab c

x

-3

y

O Ew_Ew_

3

2

x=^3

y= 2 x- 3

y

x

()-4 ¡4,

()3 -2,

O

y

x

()-5 -145,

()-2 ¡44,

()3 -81,

O

y

x

O

O

y

2 x

2 yx¡=¦()

O

y

-1 x

2

y¡=¦()x

O

y

-2 x

1

y¡=¦()x

¡

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y:\HAESE\IGCSE01\IG01_19\398IGCSE01_19.CDR Friday, 10 October 2008 10:21:49 AM PETER