Cambridge International Mathematics

416 Transformation geometry (Chapter 20)

8 For the following, copy and draw the required function:

a

sketch y=f(x¡2)

b

sketch y=f(x)+2

c

sketch y=^12 f(x)

d

sketch y=2f(x)

e

sketch y=¡ 2 f(x)

f

sketch y=^12 f(x)

9 The graph of y=f(x) is shown alongside.

On the same set of axes, graph:

a y=f(x) b y=¡f(x) c y=^32 f(x)

d y=f(x)+2 e y=f(x¡2)

Label each graph clearly.

10 Consider f(x)=x^2 ¡ 4 , g(x)=2f(x) and h(x)=f(2x).

a Findg(x)andh(x)in terms ofx.

b Graph y=f(x), y=g(x) and y=h(x) on the same set of axes, using a graphics calculator

if necessary.

c Describe fully the single transformation which maps the graph of y=f(x) onto the graph of

y=g(x).

d Under the mapping inc, which points are invariant?

e Find thezerosof h(x), which are the values ofxfor whichh(x)is zero.

f Describe fully the single transformation which maps the graph of y=f(x) onto the graph of

y=h(x).

If a transformation maps an object onto its image, then theinverse transformationmaps the image back

onto the object.

G THE INVERSE OF A TRANSFORMATION [5.5]

O

y

x

yx¡=¡¦()

O

y

x

yx¡=¡¦()

2

-1

y

x

O

14

-2

yx¡=¡¦()

y

x

O

14

-2

yx¡=¡¦()

y

O x

-2

2

yx¡=¡¦()

O

y

x

()2 ¡2, ()4 ¡2,

yx¡=¡¦()

x

y¡=¡-2

y

O

yx¡=¡¦()

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Y:\HAESE\IGCSE01\IG01_20\416IGCSE01_20.CDR Tuesday, 14 October 2008 4:16:37 PM PETER