Cambridge International Mathematics

712 ANSWERS

5a

ba stretch with invariantx-axis, factor^14

6a/b x-intercepts are§ 1 , y-intercept is¡ 1

cia vertical translation of

¡ 0

3

¢

iia horizontal translation of

¡ 1

0

¢

iii a stretch with invariantx-axis and scale factor 2

iv a reflection in thex-axis

d

A stretch with invariantx-axis and scale factork=¡ 2.

e(¡ 1 ,0)and(1,0)

7a iA stretch with invariantx-axis and scale factork=3.

iig(x)=3f(x)

biA vertical translation of

¡ 0

¡ 2

¢

: iig(x)=f(x)¡ 2

ciA stretch with invariantx-axis and scale factork=^12.

iig(x)=^12 f(x)

8a b

c

d

e

f

9

10 a g(x)=2x^2 ¡ 8 , h(x)=4x^2 ¡ 4

b

c A stretch with invariantx-axis andk=2.

d (¡ 2 ,0)and(2,0) e zeros are§ 1

f A stretch with invarianty-axis andk=^12.

EXERCISE 20G

1aa reflection in they-axis

b a rotation about O(0,0)through 180 o

x

-2 2

44

22

y=f(x- 1 )

y=f(x)+ 3

f(x)=x^2 - 1

y

x

-2 2

2

-2

y

y=- 2 f(x)

y=x^2 - 1 =f(x)

O

y

x

yx¡=¡¦()

yx¡=¡¦ ¡-¡2()

x¡=¡2

O

y

x

yx¡=¡¦()

2

-1

1

yx¡=¡¦()¡+¡2

-2

x

y¡=¡-2

y

O

yx¡=¡¦()

y¡=¡-1

yx¡=¡ ¦\Qw_\ ( )

y

O x

14

-2-2

yx¡=¡¦()

yx¡=¡2¦()

-4-4

y

x

O

14

-2-2

yx¡=¡¦()

(^44) yx¡=¡-2¦()
y
O x
-2
2
yx¡=¡¦()
1 yx¡=¡ ¦\Qw\ ( )
x
-2-2-1-1 11 22
22
11
-1-1
-2-2
y
y= 2 f(x)
y=-f(x)
y=f(x)=x^2 - 1
x
1 2
-2 -1
2
1
-1
-2
y
y= 2 h(x)
y= 21 h(x)
h(x)=x^3
O
y
x
yx¡=¡¦()
yx¡=¡ ¦\Ew\ ( )
yx¡=¡¦()¡+¡2
yx¡=¡¦ ¡-¡2()
yx¡=¡-¦()
2
-2
2
x
-6-6 -4-4 -2-2 22 44 66
22
-2-2
-4-4
-6-6
-8-8
y
yhx¡=¡()
yxx¡=¡¦() X¡=¡ ¡-¡4
ygx¡=¡()
IB MYP_3 ANS
cyan magenta yellow black
(^05255075950525507595)
100 100
(^05255075950525507595)
100 100
Y:\HAESE\IGCSE01\IG01_an\712IB_IGC1_an.CDR Thursday, 20 November 2008 4:33:38 PM PETER