Cambridge International Mathematics

ANSWERS 711

3a(4^12 ,6)

b(0,2)

4a iy=2x ii y=2x

biy=¡x+8 ii y=¡x+^43

ciy=2x+9 ii y=2x

EXERCISE 20E

1a b

c

d

2a b

3a(3,¡4) b(4,10) c(¡ 1 ,1) d(4^12 ,¡4)

e(^34 , 134 )

4a

A^0 is(1,3),B^0 is(4,1)

C^0 is(2,9)

b

A^0 is(0,2),B^0 is(1^12 ,1)

C^0 is(^12 ,5)

5aVertical stretch of factor k=^34 with invariantx-axis.

bHorizontal stretch of factork=2, with invarianty-axis.

cHorizontal stretch of factork=4, with invarianty-axis.

dHorizontal stretch of factork=^14 , withx=¡ 1 the

invariant line.

6ay=6x b y=^94 x cy=^14 x+2^14

EXERCISE 20F

1a

by¡=f(x)+4is a vertical translation ofy=f(x)through

0

4

¢

.

y=f(x+4) is a horizontal translation of y=f(x)

through

¡¡ 4

0

¢

.

2a

bia horizontal translation of

¡ 3

0

¢

ii a translation of

¡ 3

1

¢

3a

by=¡ 1

c

y=¡ 1

4a

bpoints on thex-axis, i.e., (^12 ,0)

IL

A B

C

A'

B'

C'

IL

A

B

C

D

A'

B'

D'

C'

IL

P

Q

R

S

R'

S'

Q'

P'

IL

Y' X

Z

W

Z' X'

W'

Y

y

x

O

x¡=¡1

IL

2

2

A

B

C

k¡=¡¡Ew_

B'

A' C'

y

x

O

2

IL

y¡=¡-2

P

Q

R

S

k¡=¡¡Qw_

2

R'

S' Q'

P'

y

O 246

2

4

6

8

A

A' B' B

C'C

x

-2

y x¡=¡-1

O 246

2

4

6

8

A

A'

B

B'

C

C'

-2 x

y¡=¡1

x

4

-4

10

-2

y

yx¡=¡3 ¡-¡2¡=¡¦()x

yx¡=¡¦ ¡+¡4()

yx¡=¡¦()¡+¡4

x

-4 -2 2 4

6

4

2

y

y¡=¡-1

y¡=¡2 ¡=¡¦x ()x

yx= ¦ ¡-¡3()

yx= ¦()¡-¡1

11 ()3 ¡1,

2 x

-2

2

y

yx¡=¡2 ¡-¡1¡=¡¦()x

yxx¡=¡3¦()¡=¡6 ¡-¡3

(\Qw_\' 0)

-2-2

x

-2 2 4

6

4

2

y

y¡=¡-1

ygx¡= ¡\(Qw_\)x¡=¡( )

yx=g()¡-¡1

6

11

x

-1 11 22 33

44

33

22

11

-1-1

-2-2

y

O

y=g(x)- 1 =(^12 )x-^1 - 1

y=g(x)=(^12 )x-^1

IB MYP_3 ANS

cyan magenta yellow black

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Y:\HAESE\IGCSE01\IG01_an\711IB_IGC1_an.CDR Thursday, 20 November 2008 4:30:03 PM PETER