Cambridge International Mathematics

414 Transformation geometry (Chapter 20)

What to do:

1 On the same set of axes graph:

a y=

1

x

b y=

1

x

+2 c y=

1

x

¡ 3 d

What transformation maps y=

1

x

onto y=

1

x

+k?

2 On the same set of axes graph:

a y=

1

x

b y=

1

x+2

c y=

1

x¡ 3

d y=

1

x+4

What transformation maps y=

1

x

onto y=

1

x+k

?

You should have discovered that:

² y=f(x) maps onto y=f(x)+k under avertical translationof

¡ 0

k

¢

² y=f(x) maps onto y=f(x+k) under ahorizontal translationof

¡¡k

0

¢

² y=f(x) maps onto y=kf(x) under a stretch with invariantx-axis and scale factork.

Example 11 Self Tutor

Consider f(x)=^12 x+1. On separate sets of axes graph:

a y=f(x) and y=f(x+2) b y=f(x) and y=f(x)+2

c y=f(x) and y=2f(x) d y=f(x) and y=¡f(x)

ab

cd

O

y

x

-2

-2

11

-2

-2

-2 yx¡=¡¦()

yx¡=¡¦ ¡+¡2()

22

O

y

-2 x

+2^11

+2

+2

+2

yx¡=¡¦()

yx¡=¡¦()¡+¡2

33

O

y

x

11

-2-2

yx¡=¡¦()

yx¡=¡2¦()

22

O

y

x

11

-2-2

-1-1

yx¡=¡¦()

yx¡=¡-¦()

y=

1

x

+5

3 On the same set of axes graph:

a y=

1

x

b y=

2

x

c y=

3

x

d y=

¡ 1

x

e y=

¡ 4

x

What transformation maps y=

1

x

onto y=

k

x

?

IGCSE01

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Y:\HAESE\IGCSE01\IG01_20\414IGCSE01_20.CDR Tuesday, 18 November 2008 10:59:24 AM PETER