Cambridge International Mathematics

ANSWERS 707

EXERCISE 19A

1a b

cd

e

2afreal numbersg

bfmultiples of 2 which are not multiples of 4 g

cfpositive real numbersg dfreal numbers> 10 g

efall integersg

EXERCISE 19B.1

1aDomain=f¡ 3 ,¡ 2 ,¡ 1 , 0 , 6 g Range=f¡ 1 , 3 , 4 , 5 , 8 g.

bDomain=f¡ 3 ,¡ 1 , 0 , 2 , 4 , 5 , 7 g Range=f 3 , 4 g.

2aDomain isfxjx>¡ 4 g. Range isfyjy>¡ 2 g.

Is a function.

bDomain isfxjx=2g. Range is fyjyis inRg.

Is not a function.

cDomain isfxj¡ 36 x 63 g. Range isfyj¡ 36 y 63 g.

Is not a function.

dDomain isfxjxis inRg. Range isfyjy 60 g.

Is a function.

eDomain isfxjxis inRg. Range isfyjy=¡ 5 g.

Is a function.

fDomain isfxjxis inRg. Range isfyjy> 1 g.

Is a function.

gDomain isfxjxis inRg. Range isfyjy 64 g.

Is a function.

hDomain isfxjx>¡ 5 g. Range isfyjyis inRg.

Is not a function.

i Domain isfxjx 6 =1,xis inRg.

Range is fyjy 6 =0,yis inRg.

Is a function.

3af 2 , 3 , 5 , 10 , 12 g b f 0 ,^12 , 2 g

cfyj¡ 3 <y< 5 g d fyj¡ 276 y 664 g

4a i

ii Range is

fyj¡ 56 y 67 g.

bi

iiRange is

fyj 06 y 616 g.

ci

iiRange is

fyj¡ 96 y 611 g.

di

iiRange is

fyjy 6 ¡ 1 ory>^12 g.

ei

ii Range is

fyjy 6 ¡ 2 ory> 2 g.

fi

iiRange is

fyjy> 1 g.

gi iiRange is

fyjy 2 Rg

EXERCISE 19B.2

1a,b,eare functions as no two ordered pairs have the same

x-coordinate.

2a,b,d,e,g,h,iare functions.

3 No, a vertical line is not a funtion as it does not satisfy the vertical

line test.

EXERCISE 19C

1af(5) = 8 which means that 5 is mapped onto 8 and(5,8)

lies on the graph of the functionf.

bg(3) =¡ 6 which means that 3 is mapped onto¡ 6 and

(3,¡6)lies on the graph of the functiong.

cH(4) = 4^13 which means that 4 is mapped onto 413 and

(4, 413 )lies on the graph of the functionH.

2a i 5 ii ¡ 7 iii 21 iv ¡ 395

bi 6 ii 4 iii¡ 4 iv 10

ci¡ 2 ii 212 iii 137 iv 107

3a if(4) =¡ 11 iix=§ 2 bi^12 ii a=19

cix=§

p

3 iix=§ 2 dx=¡ 8

4aV(4) = $12 000, the value of the car after 4 years.

bt=5; the car is worth$8000after 5 years. c $28 000

dNo, as when t> 7 , V(t)< 0 which is not valid.

one-one

¡ 2

0

7

xy

¡ 5

9

¡ 9

one-many

0

1

4

x y

1

¡ 1

2

0

¡ 2

many-many

0

1

2

3

0

1

2

3

xy

one-one

-2 -1 0 1 2 3 4 5 6 7

-2 -1 0 1 2 3 4 5 6 7

many-many

0

1

2

3

0

1

2

3

xy

x

-2 2

7

-5

y

()2 ¡7,

()-2 -5,

yx¡=¡3 ¡+¡1

O

x

-3 4

16

9

y

yx¡=¡X

()-3 ¡9,

()4 ¡16,

O

(^113)
-1
y
x
1
y=x- 1
x¡=¡1
(3 ¡,Qw)
O
x
y
11
yx¡=¡ ¡+¡1X
O
4 x
-4
y 1
yx
x
=+
(-4,-4Qr)
(\4, 4Qr_)
()-1 -2,
()1 ¡2,
O
-1 1 x
1
-1
y yx¡=¡C
O
x
-5 5
10
5
-5
-10
y
O
()3 ¡11,
()-2 -9,
yx¡=¡4 ¡-¡1
IB MYP_3 ANS
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(^05255075950525507595)
100 100
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Y:\HAESE\IGCSE01\IG01_an\707IB_IGC1_an.CDR Wednesday, 19 November 2008 10:22:51 AM PETER