unit 5 review for final
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____
1. Consider the relation represented by this arrow diagram. Represent the relation as a set of ordered pairs.
is the number of
people living in
a.
b.
c.
d.
____
3
House R
4
House P
1
House Q
5
House S
{(House P, 1), (House Q, 3), (House R, 4), (House S, 5)}
{(3, House P), (4, House Q), (1, House R), (5, House S)}
{(1, House P), (3, House Q), (4, House R), (5, House S)}
{(House P, 3), (House Q, 4), (House R, 1), (House S, 5)}
2. Consider the relation represented by this graph. Represent the relation as a set of ordered pairs.
Distances Driven to Work
Jodi
Student
Shadi
Tony
Koko
Josh
0
a.
b.
c.
d.
____
1
2
3
4 5 6 7 8
Distance (km )
9 10 11 12
{(5, Jodi), (7, Shadi), (4, Tony), (8, Koko), (1, Josh)}
{(Jodi, 7), (Shadi, 5), (Tony, 4), (Koko, 8), (Josh, 1)}
{(Jodi, 5), (Shadi, 7), (Tom, 4), (Koko, 8), (Steven, 1)}
{(Jodi, 5), (Shadi, 7), (Tony, 4), (Koko, 8), (Josh, 1)}
3. Consider the relation represented by this graph. Represent the relation as a set of ordered pairs.
11
Distances Jogged in a Day
10
9
Distance (km)
8
7
6
5
4
3
2
Jodi
Shadi
Tony
Koko
0
Josh
1
Student
a.
b.
c.
d.
4. Consider the relation represented by this graph. Represent the relation as a table.
12
Shoe Sizes of Students
11
10
9
8
Shoe Size
7
6
5
4
3
2
Natalie
Martin
0
Kelly
1
John
____
{(Josh, 8), (Koko, 5), (Tony, 4), (Shadi, 11), (Jodi, 7)}
{(8, Josh), (5, Koko), (Tony, 4), (11, Shadi), (Jodi, 7)}
{(8, Josh), (5, Koko), (4, Tony), (11, Shadi), (7, Jodi)}
{(Josh, 8), (Koko, 5), (Tony, 4), (Shadi, 7), (Jodi, 11)}
Student
a.
c.
b.
____
d.
5. The graph and the arrow diagram represent the same relation. The graph is correct but the arrow diagram is
not. Which pairing in the arrow diagram is correct?
12
Shoe Sizes of Students
11
has a shoe size of
10
9
Shoe Size
8
7
6
John
5
Kelly
6
Martin
8
Natalie
9
5
4
3
2
Natalie
Martin
Kelly
0
John
1
St u d e n t
a. John, 9
____
b. Natalie, 6
d. Martin, 8
6. Which ordered pair belongs to the relation shown in the diagram below?
English
w ords
has this number
of vow els
a. (function, 4)
b. (arrow, 4)
____
c. Kelly, 8
Natural
numbers
c. (relation, 4)
d. (mathematics, 2)
7. Capital cities can be associated with the province or territory they are in.
Capital City
Victoria
Edmonton
Regina
Winnipeg
Whitehorse
Yellowknife
Iqaluit
Province/Territory
British Columbia
Alberta
Saskatchewan
Manitoba
Yukon
Northwest Territories
Nunavut
Describe this relation in words.
a. The relation shows the association “is the capital of” from a set of capital cities to a set of
provinces and territories.
b. The relation shows the association “is the largest city of” from a set of capital cities to a
set of provinces and territories.
c. The relation shows the association “is the capital of” from a set of provinces and territories
to a set of capital cities.
d. The relation shows the association “is in the province/territory of” from a set of provinces
and territories to a set of capital cities.
____
8. Which arrow diagram shows the association “is less than” from a set of numbers to a set of numbers?
a.
c.
is less than
is less than
11
9
9
11
14
11
11
14
18
14
14
18
b.
d.
is less than
____
is less than
9
9
9
11
11
11
11
14
14
14
14
18
18
18
9. Which set of ordered pairs does not represent a function?
i)
ii)
iii)
iv)
a. i
b. ii
c. iv
d. iii
____ 10. Identify the domain of this relation.
a.
b.
c.
d.
____ 11. Identify the range of this relation.
1
3
6
8
9
–2
0
3
5
a.
b.
c.
d.
____ 12. This table shows the masses, m grams, of different numbers of identical beads, n. Identify the domain.
Number of Beads,
n
1
2
3
4
5
Mass of Beads, m
(g)
1.56
3.12
4.68
6.24
7.80
a.
b.
c.
d.
____ 13. This table shows the cost, C dollars, of different numbers of tickets sold, n. Identify the range.
Number of Tickets,
n
1
2
3
4
5
a.
Cost, C
($)
12.50
25.00
37.50
50.00
62.50
b.
c.
d.
____ 14. For the function
a. 7
, determine
b. 2
c. 14
____ 15. For the function
a. 83
____ 16. For the function
a. –2.2
____ 17. For the function
a. –3
____ 18. Write
.
d. 3
, determine x when
b. –67
.
d. –11
c. 11
, determine
.
c. –3.6
b. 2.2
, determine x when
c. –39
b. 12
d. 6.2
.
d. –12
in function notation.
a.
b.
c.
d.
____ 19. The function
converts a temperature, f degrees Fahrenheit, to C degrees Celsius.
Determine
to the nearest degree.
a. 38 C
b. 102 C
c. 4 C
d. –4 C
____ 20. Identify the independent variable and the dependent variable for this table of values.
Hours Worked,
h
4
5
9
20
30
a. independent variable: P
dependent variable: h
b. independent variable: domain
dependent variable: range
Gross Pay, P
($)
38.00
47.50
85.50
190.00
285.00
c. independent variable: gross pay
dependent variable: hours worked
d. independent variable: hours worked
dependent variable: gross pay
____ 21. Each point on this graph represents a person. Which two people are the same age?
Ages and Masses of People
F
80
E
G
Mass (kg)
60
C
D
40
B
20
A
0
4
8
12
Age (years)
16
20
a. E and F
b. C and D
c. D and E
d. B and C
____ 22. Each point on this graph represents an animal. Which animal has the least mass?
Ages and Masses of Anim als
F
80
E
G
Mass (kg)
60
C
D
40
B
20
0
a. C
A
4
8
12
Age (years)
b. A
16
20
c. D
d. E
____ 23. Joshua went on a bike ride. Which statement best describes what is happening for line segment DE in this
graph?
Joshua's Bike Ride
C
Distance from home (km)
5
D
4
3
A
B
2
1
E
O
a.
b.
c.
d.
20
40
60
80
Tim e (m in)
100
120
Joshua spends time at the park.
Joshua leaves home.
Joshua cycles to the park.
Joshua returns home.
____ 24. Joshua went on a bike ride. During the ride, he stopped to play at a park, as shown by line segment CD. How
much time did Joshua spend at the park?
Joshua's Bike Ride
C
Distance from home (km)
5
D
4
3
A
B
2
1
E
O
a. 65 min.
20
40
60
80
Tim e (m in)
b. 75 min.
100
120
c. 70 min.
d. 80 min.
____ 25. A person in a car drives away from a stop sign, cruises at a constant speed, and then slows down as she
approaches another stop sign. Which graph best represents this situation?
a.
c.
Speed (km/h)
Speed (km/h)
Tim e (m in)
Speed (km/h)
d.
Speed (km/h)
b.
Tim e (m in)
Tim e (m in)
Tim e (m in)
____ 26. This graph shows the height of the tide in a harbour as a function of time in one day. What is the greatest
height of the tide?
Height of the Tide in a Harbour
10
Height (m)
8
6
4
2
0
00:00
03:00
06:00
a. 9 m
09:00
12:00
15:00
Tim e (24-h clock)
b. 2 m
18:00
c. 8 m
21:00
24:00
d. 4 m
____ 27. This graph shows the free-fall speed of a skydiver as a function of time. At what speed was the skydiver
travelling 10 s before she reached the ground?
Free-Fall Speed of a Skydiver
160
A
B
Speed (km/h)
120
80
40
D
C
O
E
5 10 15 20 25 30 35 40 45 50 55 60 65
Tim e (s)
a. 20 km/h
b. 140 km/h
c. 30 km/h
d. 10 km/h
____ 28. This graph shows the free-fall speed of a skydiver as a function of time. About how long did the skydiver’s
jump last?
Free-Fall Speed of a Skydiver
160
A
B
Speed (km/h)
120
80
40
D
C
O
E
5 10 15 20 25 30 35 40 45 50 55 60 65
Tim e (s)
a. About 20 s
b. About 13 s
c. About 60 s
d. About 63 s
____ 29. This graph shows the free-fall speed of a skydiver as a function of time. Which statement best describes what
is happening for line segment BC in the graph?
Free-Fall Speed of a Skydiver
160
A
B
Speed (km/h)
120
80
40
D
C
O
a.
b.
c.
d.
E
5 10 15 20 25 30 35 40 45 50 55 60 65
Tim e (s)
The skydiver landed on the ground.
The skydiver opened her parachute.
The skydiver was free-falling.
The skydiver jumped out of the plane.
____ 30. Gail leaves the house for her morning jog. She stops for a quick drink, then continues jogging before stopping
again to chat with a friend. She then jogs back home. Which graph best represents Gail’s run?
a.
Distance from home (km)
Gail's Run
Tim e (m in)
Distance from home (km)
b.
Gail's Run
Tim e (m in)
Distance from home (km)
c.
Gail's Run
Tim e (m in)
Distance from home (km)
d.
Gail's Run
Tim e (m in)
____ 31. Which graph best represents the cost of renting a kayak as a function of time?
a.
c.
Cost ($)
Renting a Kayak
Cost ($)
Renting a Kayak
Tim e (h)
Tim e (h)
b.
d.
Cost ($)
Renting a Kayak
Cost ($)
Renting a Kayak
Tim e (h)
Tim e (h)
____ 32. Which of these graphs represents a function?
i)
ii)
y
y
x
iii)
x
iv)
y
y
x
x
a. ii
b. i
c. iii
d. iv
____ 33. Which of these graphs represents a function?
i)
ii)
y
y
x
x
iii)
iv)
y
y
x
a. iv
b. ii
____ 34. Determine the domain and range of this graph.
x
c. i
d. iii
y
4
2
–4
–2
0
2
4
x
–2
–4
a.
b.
c.
d.
____ 35. Determine the domain and range of the graph of this function.
4
y
2
–4
–2
0
y = f(x)
2
4
x
–2
–4
–6
a.
b.
c.
d.
____ 36. This graph shows the cost of parking, c, as a function of time, t. Determine the domain of the graph.
c
Cost of Parking
Cost ($)
4
3
2
1
0
30
60
90
Tim e (m in)
120
t
a.
b.
c.
d.
____ 37. This is a graph of the function
. Determine the range value when the domain value is 2.
y
4
g(x) = –2x + 3
2
–4
–2
0
2
4
x
–2
–4
a. 0.5
c. –1
b. 7
d. 1
. Determine the domain value when the range value is –4.
____ 38. This is a graph of the function
y
4
2
–4
–2
0
g(x) = –3x + 2
2
4
x
–2
–4
a. –2
b. 0.5
____ 39. This is a graph of the function
c. 11
d. 2
. Determine the domain value when the range value is –2.
y
4
2
–4
–2
0
2
4
x
–2
–4
f(x) = –2x – 4
–6
a. 3
b. 1
c. 2
d. –1
____ 40. A bathtub contains 40 L of water. The plug is pulled. This graph shows the volume of water remaining in the
tub, v, as a function of time, t. What is a restriction on the range?
v
Volum e of Water in a Tub
Volume (L)
40
30
20
10
0
60
120
180
240
300
t
Tim e (s)
a.
b.
c.
d.
The range can only contain negative numbers.
The range cannot contain negative numbers.
The range can only contain whole numbers up to 40.
The range can only contain whole numbers greater than 40.
____ 41. Determine the domain of this graph.
y
4
2
–4
–2
0
2
4
x
–2
–4
a.
b.
c.
d.
____ 42. Determine the range of the graph.
y
4
2
–4
–2
0
2
4
x
–2
–4
a.
b.
c.
d.
____ 43. Which table of values represents a linear relation?
i)
Distance (m) 0 5 10 15 20
0 1 2 3 4
Time (s)
ii)
Time (s)
Distance (m)
0 3 6 9 12
0 10 22 36 52
iii)
Time (s)
Speed (m/s)
iv)
0 1
0 1
2
2
3
4
4
8
0 4
0 2
Distance (m)
Speed (m/s)
a. iii
16 36 64
4 6 8
b. i
c. ii
d. iv
____ 44. The relation between x and y is linear. Which number would complete this table?
3
19
x
y
7
13
a. –7
11
7
15
19
–5
c. –6
b. 1
d. 6
____ 45. This graph represents a 150-L hot-water tank being filled at a constant rate. Determine the rate of change of
the relation.
V
Filling a Hot-Water Tank
175
(50, 150)
Volume (L)
150
125
100
75
(25, 75)
50
25
0
10
20
30
40
Tim e (m in)
50
t
a. 25 L/min
b. 3 L/min
c. 75 L/min
d. 0.33 L/min
____ 46. This table of values represents a linear relation. Determine the rate of change of the relation.
Time (s)
Distance (m)
a. 5 m/s
0
0
1
5
2
10
3
15
b. 10 m/s
4
20
c. 2 m/s
d. 1 m/s
____ 47. The altitude of a plane, a metres, is related to the time, t minutes, that has elapsed since it started its ascent.
Determine the rate of change of this linear relation.
t (min)
a (m)
a. 1500 m/min
0
4000
2
5400
b. 1400 m/min
4
6800
6
8200
8
9600
c. 1200 m/min
d. 700 m/min
____ 48. Minerva has $100. This graph represents the money Minerva would have if she purchased different numbers
of CDs. Determine the rate of change of the relation.
m
Minerva's CDs
Money remaining ($)
100
80
60
40
20
0
1
a.
b.
2
3
4
5
6
Num ber of CDs purchased
/CD
/CD
7
8
c.
d.
n
/CD
/CD
____ 49. This set of ordered pairs represents a linear relation. Determine its rate of change.
a.
c.
3
7
b.
7
3
d.
7
3
3
7
____ 50. The monthly income, I dollars, of a furniture salesperson is given by the equation
, where s
represents the salesperson’s total monthly sales in dollars. Determine the rate of change of this linear relation.
a. 0.03
b. 33.3
c. 1500
d. 3
____ 51. This graph represents the boiling point of water, b degrees Celsius, as a function of altitude, a metres. Identify
the independent variable.
b
Boiling Point of Water
100
Boiling point (ºC)
80
60
40
20
0
4000
8000 12 000 16 000 20 000 24 000
Altitude (m )
a
a. m
b. a
c. b
d. C
____ 52. Which set of ordered pairs represents a linear relation?
i)
ii)
iii)
iv)
a. iv
b. i
c. ii
d. iii
____ 53. For a service call, an electrician charges a $65 flat fee, plus $45 for every 30 min worked. Determine the rate
of change of this linear relation.
a. $45/h
b. $110/h
c. $65/h
d. $90/h
____ 54. Which equation does not represent a linear relation?
i)
ii)
iii)
iv)
a. iii
b. ii
c. i
d. iv
____ 55. This graph shows distance, d kilometres, as a function of time, t minutes. Determine the vertical and
horizontal intercepts.
d
d = f(t)
Distance (km)
100
80
60
40
20
20
40
60
80
100
Tim e (m in)
120
t
a. Vertical intercept: 80
Horizontal intercept: 96
c. Vertical intercept: 96
Horizontal intercept: 80
b. Vertical intercept: 64
d. Vertical intercept: 80
Horizontal intercept: 96
Horizontal intercept: 64
____ 56. This graph shows the volume of water remaining in a leaking hot tub as a function of time. Determine the
domain and range.
V
W a t e r i n a L e a k i n g Ho t T u b
2400
Vo lu m e ( L )
2000
1600
1200
800
400
0
24
48
72
96
120
Tim e (h)
a. Domain:
Range:
b. Domain:
Range:
144
168
192
216
t
c. Domain:
Range:
d. Domain:
Range:
____ 57. Which graph represents the linear function
?
a.
c.
y
–4
b.
–2
y
4
4
2
2
0
2
4
–4
x
–2
0
–2
–2
–4
–4
d.
2
4
x
y
–4
–2
y
4
4
2
2
0
2
4
–4
x
–2
0
–2
–2
–4
–4
2
4
x
____ 58. Each graph below shows distance, d metres, as a function of time, t hours. Which graph has a rate of change
of 4 m/h and a vertical intercept of 3 m?
a.
c.
10
d
10
8
Distance (m)
Distance (m)
8
d
6
4
d = k(t)
6
4
d = g(t)
2
2
2
4
6
Tim e (h)
8
0
t
b.
2
4
6
Tim e (h)
8
t
4
6
Tim e (h)
8
t
d.
10
d
10
8
Distance (m)
Distance (m)
8
d
6
4
6
4
d = h(t)
d = f(t)
2
0
2
2
4
6
Tim e (h)
8
t
0
2
____ 59. Each graph below shows distance, d metres, as a function of time, t hours. Which graph has a rate of change
of 0.75 m/h and a horizontal intercept of 3 m?
a.
c.
10
d
10
8
Distance (m)
Distance (m)
8
d
6
4
6
4
d = h(t)
2
2
0
0
d = g(t)
2
4
6
Tim e (h)
8
t
b.
2
4
6
Tim e (h)
8
t
4
6
Tim e (h)
8
t
d.
10
d
10
8
Distance (m)
Distance (m)
8
6
4
2
6
4
2
d = f(t)
0
d
2
4
6
Tim e (h)
d = k(t)
8
t
0
2
____ 60. The graph shows the cost of hosting an anniversary party. What is the maximum number of people who can
attend the party for a cost of $1500?
Cost of an Anniversary Party
C
2100
1800
Cost ($)
1500
1200
900
600
300
0
10
20
30
40
50
Num ber of people
a. 61 people
b. 38 people
60
n
c. 33 people
d. 27 people
____ 61. This graph shows the cost of a taxi ride. The cost, C dollars, is a function of the duration of the ride, t min.
What is the duration of the ride when the cost is $35?
C
C o s t o f a T a x i Ri d e
50
Cost ($)
40
30
20
10
0
10
20
30
40
50
Tim e (m in)
a. 45 min
b. 58 min
60
c. 50 min
d. 53 min
____ 62. Which graph represents the linear function
a.
70 t
?
c.
y
–4
–2
y
4
4
2
2
0
2
4
–4
x
–2
0
–2
–2
–4
–4
b.
2
4
x
2
4
x
d.
y
–4
–2
y
4
4
2
2
0
2
4
x
–4
–2
0
–2
–2
–4
–4
____ 63. This graph shows the cost of gas. The cost, C dollars, is a function of the volume, V litres, of gas purchased.
What is the volume of gas purchased when the cost is $10.45?
14
The Cost of Gas
C
12
Cost ($)
10
8
6
4
2
0
2
4
6
8
Volum e (L)
10
V
a. about 11.5 L
b. about 10.5 L
c. about 9.5 L
d. about 9 L
____ 64. This graph represents the time it takes to fill a 140-L hot-water tank. Determine the volume of water in the
tank after 50 min.
V
Filling a Hot-Water Tank
160
Volume (L)
120
80
40
0
10
a. about 23 L
b. about 97 L
20
30
40
50
Tim e (m in)
60
70
t
c. about 119 L
d. about 108 L
____ 65. The graph shows the height of a float plane as it descends to land. Determine the rate of change for this graph.
1800
He i g h t o f a Fl o a t P l a n e
h
Height (m)
1500
1200
900
600
300
0
2
4
6
8
10
Tim e (m in)
a. –125 m/min
b. –0.008 m/min
12
14
t
c. 125 m/min
d. –1500 m/min
____ 66. This graph shows a person’s distance from a starting point, d kilometres, as a function of time, t minutes.
Determine the distance from the starting point when the time is 5 min.
d
Di s t a n c e f r o m a S t a r t i n g P o i n t
Distance (km)
5
4
3
2
1
0
2
a. about 10.1 km
b. about 14.3 km
4
6
8
10
Tim e (m in)
12
14
t
c. about 1.8 km
d. about 0.6 km
Short Answer
67. Consider the relation represented by this arrow diagram. Represent the relation as a set of ordered pairs.
contains this number
of passengers
Car #1
1
Car #2
2
Car #3
3
Car #4
5
68. Different coloured game pieces can be associated with their lengths, in centimetres. Consider the relation
represented by this arrow diagram. Represent the relation as a graph.
has a length (cm) of
Red
Black
5
Yellow
7
Green
10
White
12
Blue
69. The set of ordered pairs below shows Aboriginal ice-hockey players who have played in the NHL and their
heritage. Represent the relation as a table.
{(Jordin Tootoo, Inuit), (Jonathan Cheechoo, Moose Cree), (Sheldon Souray, Metis),
(Wade Redden, Metis), (Chris Simon, Ojibwa), (Sandy McCarthy, Mi’kmaq)}
70. Use the numbers below.
a) Write a set of ordered pairs that represents a function.
b) Write a set of ordered pairs that does not represent a function.
71. Identify the domain and range of this relation.
is a factor of
3
4
5
2 520
6
7
72. This graph shows how the volume of water in a barrel changes over time.
Volum e of Water in a Barrel
Volume (L)
30
20
10
10
20
30
Tim e (m in)
40
50
a) About how much water was in the barrel after 25 min?
b) After how many minutes was the barrel empty?
73. The graph shows the speed of a windsurfer as a function of time.
Speed of a Windsurfer
50
B
C
Speed (km/h)
40
30
A
20
D
10
E
O
2
4
6
Tim e (s)
8
10
a) For how long did the windsurfer travel at a speed of 45 km/h?
b) How long did the windsurfer’s ride last?
74. Natasha spent part of the afternoon running errands. This graph shows her distance from home as a function
of time.
Natasha's Drive
Distance from home (km)
8
7
6
C
5
D
4
3
2
A
B
1
E
O
5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100105110115
Tim e (m in)
a) How far did Natasha drive in total?
b) How long was Natasha away from home?
75. This graph shows the volume of gas in a car as a function of time. Describe what is happening for line
segment EF in the graph.
Volum e of Gas in a Car
Volume of gas (L)
80
E
A
F
60
G
C
40
B
20
D
0
2
4
6
8
10
Tim e from start of journey (h)
12
76. This table shows the refund, r dollars, for different numbers of juice tetra paks, n. Is this relation a function?
Explain.
Number of Juice Tetra
Paks, n
5
12
17
24
30
Refund, r ($)
0.25
0.60
0.85
1.20
1.50
77. Suppose a student drew a graph of each function described below. For which graphs should the student
connect the points?
a) The mass of a stack of coins is a function of the number of coins.
b) The temperature in Vancouver is a function of the time of day.
c) The mass of an animal is a function of its age.
d) The price of a carton of milk is a function of the size of the carton.
78. This is a graph of the function
.
y
4
2
–4
–2
0
h(x) = –1/2x + 1
2
4
x
–2
–4
a) Determine the range value when the domain value is –2.
b) Determine the domain value when the range value is –1.
79. Determine the domain and range of the graph of this function.
4
y
2
–4
–2
0
2
y = f(x)
4
x
–2
–4
–6
80. The set of ordered pairs below represents a linear relation. Determine the value of n.
81. Which equations represent linear relations? Create tables of values if necessary.
a)
b)
c)
d)
e)
f)
82. This table represents the approximate relation between a distance in miles and the same distance in
kilometres. Determine the rate of change of the relation..
Miles (mi.)
Kilometres (km)
9
14.4
18
28.8
27
43.2
83. Which graphs have:
i) a negative rate of change?
ii) a positive rate of change?
iii) neither a negative nor a positive rate of change?
a)
b)
36
57.6
45
72.0
y
–4
–2
y
4
4
2
2
0
2
4
–4
x
–2
0
–2
–2
–4
–4
c)
2
4
x
2
4
x
2
4
x
d)
y
–4
–2
y
4
4
2
2
0
2
4
–4
x
–2
0
–2
–2
–4
–4
e)
f)
y
–4
–2
y
4
4
2
2
0
2
4
x
–4
–2
0
–2
–2
–4
–4
84. A quarter has a mass of 4.4 g. This graph represents the mass of a stack of quarters as a function of the
number of quarters in the stack. Identify the independent and dependent variables.
m
Mass of Quarters
24
20
Mass (g)
16
12
8
4
0
1
2
3
4
Num ber of quarters
5
n
85. This graph shows the volume of gasoline left in a car’s tank, v litres, as a function of the distance travelled, d
in hundreds of kilometres. Determine the domain and range of the graph.
Fuel left in tank (L)
v
Ra t e o f Fu e l C o n s u m p t i o n
72
60
48
36
24
12
1
2
3
4
5
6
Di s t a n c e ( 1 0 0 s o f k m )
7
86. Determine the vertical and horizontal intercepts of this graph.
d
y
4
y = f(x)
2
–4
–2
0
2
4
x
–2
–4
87. Determine the rate of change and the vertical intercept of this graph.
y
4
y = f(x)
2
–4
–2
0
2
4
x
–2
–4
Problem
88. Consider the relation represented by this arrow diagram.
divided by 9 is
81
9
90
10
99
11
108
12
117
13
a) Represent the relation as a set of ordered pairs.
b) Does the order of the numbers in each ordered pair matter? Explain.
89. The equation
a) Describe the function.
represents the total cost, C dollars, for a sports banquet when g people attend.
Write the function in function notation.
b) Determine C(46).
What does this number represent?
c) Determine the value of g when C(g) = 1581.
What does this number represent?
90. A gas station attracts customers by offering coupons worth $0.03 for every $1.00 spent on gasoline.
Value of Gas
Purchase, v
($)
1
2
Value of
Coupons, c
($)
0.36
20
1.20
50
a)
b)
c)
d)
Use function notation to express c as a function of v.
Copy and complete the table.
What is the value of the coupons a customer will receive if she spends $80 on gasoline?
How much does a customer have to spend on gasoline to receive $5.00 in coupons?
91. This graph shows the volume of water in Katherine’s water bottle as she cycles around town. Describe what is
happening for line segments FG, HI, and KL in the graph.
Volum e of Water in a Bottle
2.5
2
A
B
I
J
Volume (L)
D
1.5
L
C
K
F
1
E
0.5
G
H
M
10
20
30
40
50
Distance from hom e (km )
92. An oven is turned on at a room temperature of 20 C and it takes 10 min to reach a temperature of 190 C. A
cake is placed in the oven to bake for 30 min. The oven is then turned off and returns to room temperature
after 15 min. The oven is turned on again 45 min later and it takes 15 min to reach a temperature of 160 C.
Cookies are placed in the oven to bake for 20 min. The oven is then turned off and returns to room
temperature after 15 min. Sketch a graph of temperature as a function of time. Label each section of the graph
and explain what it represents.
93. This graph represents a day trip from Vancouver to Hope, B.C. The distance between Vancouver and Hope is
approximately 150 km.
a) Describe the journey for each segment of the graph.
b) How long did the day trip take?
c) What are the dependent and independent variables?
Day Trip from Vancouver to Hope
180
165
C
150
D
Distance (km)
135
120
105
A
B
90
E
75
F
60
45
30
15
G
O
1
2
3
Tim e (h)
4
94. For this table of values:
a) Graph the data. Will you join the points? Justify your answer.
b) Does the graph represent a function? Explain?
5
6
7
Number of People, n
15
30
60
90
120
Cost, C
($)
0.50
1.00
2.00
3.00
4.00
95. A bathtub contains 40 L of water. The plug is pulled. The volume of water remaining in the tub is recorded at
various intervals.
Time
(s)
0
55
105
170
225
300
Volume
(L)
40.0
26.7
16.9
7.5
2.5
0.0
Graph the data. Show volume as a function of time. Will you join the points? Explain.
96. Four litres of latex paint covers approximately 37 m2 and costs $52.
a) Copy and complete this table.
Volume of Paint, p (L)
Cost, c ($)
Area Covered, A (m2)
0 4
0 52
0 37
8
12
16
b) Graph the area covered as a function of the volume of paint.
c) Graph the area covered as a function of the cost.
d) Write the domain and range of the functions in parts b and c.
97. This table shows the volume of water in a barrel that is leaking at a constant rate.
Time, t
(min)
0
10
30
40
60
75
Volume of Water,
V (L)
60
52
36
28
12
0
A student drew a graph of the function.
V
Water in a Barrel
Volume of water (L)
100
80
60
40
20
20
40
60
Tim e (m in)
80
100 t
a) Describe any errors in the graph.
b) Write the domain and range of the graph.
98. a) This is a graph of the function
.
Determine the range value when the domain value is 2.
y
4
f(x) = 2 x +1
–4
–2
2
0
2
4
x
–2
–4
b) This is the graph of the function
.
Determine the range value when the domain value is 3.
y
4
2
g(x) = 1 – 2x
–4
–2
0
2
4
x
–2
–4
99. A company rents paddle boats by the day. This table shows the total cost of renting a paddle boat for different
numbers of days.
Number of
Total Cost ($)
Days (n)
1
$54.00
3
$112.00
5
$170.00
7
$228.00
a) Graph the relation between the total cost of the rental and the number of days.
b) Does the graph represent a linear relation? How do you know?
c) Determine the rate of change, then describe what it represents.
100. The graph represents the cost of printing pamphlets.
c
Cost of Printing Pam phlets
360
Cost ($)
300
240
180
120
60
0
4
8
12
16
20
Num ber of pam phlets (hundreds)
n
a) Identify the dependent and independent variables.
b) Sohan calculated the rate of change as follows:
Change in cost:
Change in number of pamphlets: 2000 pamphlets – 500 pamphlets = 1500 pamphlets
Rate of change:
Did he calculate the rate of change correctly? Explain.
c) Describe what the rate of change represents.
101. A helicopter is travelling toward its destination.
Time (min)
0
20
40
60
80
a)
b)
c)
d)
Distance from
Destination (mi.)
285
244
203
162
121
Identify the dependent and independent variables.
Use the table of values to determine whether the relation is linear.
If the relation is linear, determine its rate of change.
Assume the helicopter continues to travel at the same speed. How many more minutes will it take the
helicopter to reach its destination? Give your answer to the nearest minute.
102. A skydiver jumps from an altitude of 3700 m. For the first 12 s, her height in metres above the ground is
described by this set of ordered pairs:
. Between 18 s and 36 s,
her height above the ground is described by this set of ordered pairs:
.
Determine whether either set of ordered pairs represents a linear relation. Explain.
103. This graph shows the time it takes to fill a gas tank from empty.
t
Tim e to Fill a Gas Tank
140
120
Time (s)
100
80
60
40
20
0
10
20
30
40
50
60
Volum e (L)
70
80
90
v
a) Determine the vertical and horizontal intercepts. Write the coordinates of the point where the graph
intersects the axes. Describe what the point represents.
b) Determine the rate of change. What does it represent?
c) Write the domain and range.
d) About how long will it take to fill a 45-L gas tank?
104. This graph shows the length, l metres, of an object’s shadow as a function of the height of the object, h
metres.
l
Length of an Object's Shadow
70
Length of shadow (m)
60
50
40
30
20
10
0
4
8
12
16
20
24
Height of object (m )
28
32
36
h
a) What is the rate of change? What does it represent?
b) A tree has height 13 m. About how long is its shadow?
c) The length of the shadow of a building is 45 m. About how tall is the building?
105. Sketch a graph of the linear function
.
106. This graph shows the distance, d kilometres, from Beijing, China, to Edmonton, Alberta, as a function of
flying time, t hours.
9000
d
F l i g h t f r o m B e i j Ed
i n gm toon t o n
8000
7000
Distance (km)
6000
5000
4000
3000
2000
1000
0
2
4
6
8
Tim e (h)
10
12 t
a) Determine the vertical and horizontal intercepts. Write the coordinates of the points where the graph
intersects the axes. Describe what the points of intersection represent.
b) Determine the rate of change. What does it represent?
c) Write the domain and range?
d) What is the distance to Edmonton when the plane has been flying for 5 h?
e) How many hours has the plane been flying when the distance to Edmonton is 6500 km?
unit 5 review for final
Answer Section
MULTIPLE CHOICE
1. ANS:
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B
PTS: 1
DIF: Easy
10.RF4
TOP: Relations and Functions
D
PTS: 1
DIF: Easy
10.RF4
TOP: Relations and Functions
A
PTS: 1
DIF: Easy
10.RF4
TOP: Relations and Functions
C
PTS: 1
DIF: Easy
10.RF4
TOP: Relations and Functions
B
PTS: 1
DIF: Easy
10.RF4
TOP: Relations and Functions
C
PTS: 1
DIF: Easy
10.RF4
TOP: Relations and Functions
A
PTS: 1
DIF: Easy
10.RF4
TOP: Relations and Functions
D
PTS: 1
DIF: Moderate
10.RF4
TOP: Relations and Functions
A
PTS: 1
DIF: Easy
10.RF2
TOP: Relations and Functions
C
PTS: 1
DIF: Easy
10.RF1
TOP: Relations and Functions
C
PTS: 1
DIF: Easy
10.RF1
TOP: Relations and Functions
B
PTS: 1
DIF: Easy
10.RF1
TOP: Relations and Functions
B
PTS: 1
DIF: Easy
10.RF1
TOP: Relations and Functions
C
PTS: 1
DIF: Easy
10.RF8
TOP: Relations and Functions
C
PTS: 1
DIF: Easy
10.RF8
TOP: Relations and Functions
A
PTS: 1
DIF: Easy
10.RF8
TOP: Relations and Functions
A
PTS: 1
DIF: Easy
10.RF8
TOP: Relations and Functions
B
PTS: 1
DIF: Easy
10.RF8
TOP: Relations and Functions
C
PTS: 1
DIF: Moderate
10.RF8
TOP: Relations and Functions
D
PTS: 1
DIF: Easy
10.RF8
TOP: Relations and Functions
C
PTS: 1
DIF: Easy
5.3 Interpreting and Sketching Graphs
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5.1 Representing Relations
Conceptual Understanding
5.1 Representing Relations
Conceptual Understanding
5.1 Representing Relations
Conceptual Understanding
5.1 Representing Relations
Conceptual Understanding
5.1 Representing Relations
Conceptual Understanding
5.1 Representing Relations
Conceptual Understanding
5.1 Representing Relations
Conceptual Understanding
5.1 Representing Relations
Conceptual Understanding
5.2 Properties of Functions
Conceptual Understanding
5.2 Properties of Functions
Conceptual Understanding
5.2 Properties of Functions
Conceptual Understanding
5.2 Properties of Functions
Conceptual Understanding
5.2 Properties of Functions
Conceptual Understanding
5.2 Properties of Functions
Procedural Knowledge
5.2 Properties of Functions
Procedural Knowledge
5.2 Properties of Functions
Procedural Knowledge
5.2 Properties of Functions
Procedural Knowledge
5.2 Properties of Functions
Conceptual Understanding
5.2 Properties of Functions
Procedural Knowledge
5.2 Properties of Functions
Conceptual Understanding
LOC: 10.RF1
TOP:
22. ANS:
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37. ANS:
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Relations and Functions
KEY:
B
PTS: 1
DIF:
5.3 Interpreting and Sketching Graphs
Relations and Functions
KEY:
D
PTS: 1
DIF:
5.3 Interpreting and Sketching Graphs
Relations and Functions
KEY:
C
PTS: 1
DIF:
5.3 Interpreting and Sketching Graphs
Relations and Functions
KEY:
D
PTS: 1
DIF:
5.3 Interpreting and Sketching Graphs
Relations and Functions
KEY:
C
PTS: 1
DIF:
5.3 Interpreting and Sketching Graphs
Relations and Functions
KEY:
A
PTS: 1
DIF:
5.3 Interpreting and Sketching Graphs
Relations and Functions
KEY:
D
PTS: 1
DIF:
5.3 Interpreting and Sketching Graphs
Relations and Functions
KEY:
B
PTS: 1
DIF:
5.3 Interpreting and Sketching Graphs
Relations and Functions
KEY:
C
PTS: 1
DIF:
5.3 Interpreting and Sketching Graphs
Relations and Functions
KEY:
A
PTS: 1
DIF:
5.3 Interpreting and Sketching Graphs
Relations and Functions
KEY:
B
PTS: 1
DIF:
5.5 Graphs of Relations and Functions
Relations and Functions
KEY:
A
PTS: 1
DIF:
5.5 Graphs of Relations and Functions
Relations and Functions
KEY:
D
PTS: 1
DIF:
5.5 Graphs of Relations and Functions
Relations and Functions
KEY:
B
PTS: 1
DIF:
5.5 Graphs of Relations and Functions
Relations and Functions
KEY:
C
PTS: 1
DIF:
5.5 Graphs of Relations and Functions
Relations and Functions
KEY:
C
PTS: 1
DIF:
5.5 Graphs of Relations and Functions
Relations and Functions
KEY:
Conceptual Understanding
Easy
LOC: 10.RF1
Conceptual Understanding
Easy
LOC: 10.RF1
Conceptual Understanding
Easy
LOC: 10.RF1
Conceptual Understanding
Moderate
LOC: 10.RF1
Conceptual Understanding
Easy
LOC: 10.RF1
Conceptual Understanding
Easy
LOC: 10.RF1
Conceptual Understanding
Easy
LOC: 10.RF1
Conceptual Understanding
Moderate
LOC: 10.RF1
Conceptual Understanding
Easy
LOC: 10.RF1
Conceptual Understanding
Easy
LOC: 10.RF1
Conceptual Understanding
Easy
LOC: 10.RF2
Conceptual Understanding
Easy
LOC: 10.RF2
Conceptual Understanding
Easy
LOC: 10.RF1
Conceptual Understanding
Easy
LOC: 10.RF1
Conceptual Understanding
Easy
LOC: 10.RF1
Conceptual Understanding
Easy
LOC: 10.RF8
Conceptual Understanding
38. ANS:
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58. ANS:
D
PTS: 1
DIF: Easy
5.5 Graphs of Relations and Functions
LOC: 10.RF8
Relations and Functions
KEY: Conceptual Understanding
D
PTS: 1
DIF: Easy
5.5 Graphs of Relations and Functions
LOC: 10.RF8
Relations and Functions
KEY: Conceptual Understanding
B
PTS: 1
DIF: Easy
5.5 Graphs of Relations and Functions
LOC: 10.RF1
Relations and Functions
KEY: Conceptual Understanding
B
PTS: 1
DIF: Easy
5.5 Graphs of Relations and Functions
LOC: 10.RF5
Relations and Functions
KEY: Conceptual Understanding
B
PTS: 1
DIF: Easy
5.5 Graphs of Relations and Functions
LOC: 10.RF1
Relations and Functions
KEY: Conceptual Understanding
B
PTS: 1
DIF: Easy
REF: 5.6 Properties of Linear Functions
10.RF4
TOP: Relations and Functions
KEY: Procedural Knowledge
B
PTS: 1
DIF: Easy
REF: 5.6 Properties of Linear Functions
10.RF4
TOP: Relations and Functions
KEY: Procedural Knowledge
B
PTS: 1
DIF: Easy
REF: 5.6 Properties of Linear Functions
10.RF3
TOP: Relations and Functions
KEY: Procedural Knowledge
A
PTS: 1
DIF: Easy
REF: 5.6 Properties of Linear Functions
10.RF3
TOP: Relations and Functions
KEY: Procedural Knowledge
D
PTS: 1
DIF: Easy
REF: 5.6 Properties of Linear Functions
10.RF3
TOP: Relations and Functions
KEY: Procedural Knowledge
C
PTS: 1
DIF: Easy
REF: 5.6 Properties of Linear Functions
10.RF3
TOP: Relations and Functions
KEY: Procedural Knowledge
D
PTS: 1
DIF: Easy
REF: 5.6 Properties of Linear Functions
10.RF3
TOP: Relations and Functions
KEY: Procedural Knowledge
A
PTS: 1
DIF: Easy
REF: 5.6 Properties of Linear Functions
10.RF3
TOP: Relations and Functions
KEY: Procedural Knowledge
B
PTS: 1
DIF: Easy
REF: 5.6 Properties of Linear Functions
10.RF4
TOP: Relations and Functions
KEY: Conceptual Understanding
B
PTS: 1
DIF: Easy
REF: 5.6 Properties of Linear Functions
10.RF4
TOP: Relations and Functions
KEY: Conceptual Understanding
D
PTS: 1
DIF: Moderate
REF: 5.6 Properties of Linear Functions
10.RF3
TOP: Relations and Functions
KEY: Conceptual Understanding
C
PTS: 1
DIF: Moderate
REF: 5.6 Properties of Linear Functions
10.RF4
TOP: Relations and Functions
KEY: Procedural Knowledge
A
PTS: 1
DIF: Easy
5.7 Interpreting Graphs of Linear Functions
LOC: 10.RF5
Relations and Functions
KEY: Conceptual Understanding
D
PTS: 1
DIF: Easy
5.7 Interpreting Graphs of Linear Functions
LOC: 10.RF5
Relations and Functions
KEY: Conceptual Understanding
A
PTS: 1
DIF: Easy
5.7 Interpreting Graphs of Linear Functions
LOC: 10.RF5
Relations and Functions
KEY: Procedural Knowledge
B
PTS: 1
DIF: Easy
59.
60.
61.
62.
63.
64.
65.
66.
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5.7 Interpreting Graphs of Linear Functions
Relations and Functions
KEY:
B
PTS: 1
DIF:
5.7 Interpreting Graphs of Linear Functions
Relations and Functions
KEY:
C
PTS: 1
DIF:
5.7 Interpreting Graphs of Linear Functions
Relations and Functions
KEY:
D
PTS: 1
DIF:
5.7 Interpreting Graphs of Linear Functions
Relations and Functions
KEY:
A
PTS: 1
DIF:
5.7 Interpreting Graphs of Linear Functions
Relations and Functions
KEY:
C
PTS: 1
DIF:
5.7 Interpreting Graphs of Linear Functions
Relations and Functions
KEY:
D
PTS: 1
DIF:
5.7 Interpreting Graphs of Linear Functions
Relations and Functions
KEY:
A
PTS: 1
DIF:
5.7 Interpreting Graphs of Linear Functions
Relations and Functions
KEY:
C
PTS: 1
DIF:
5.7 Interpreting Graphs of Linear Functions
Relations and Functions
KEY:
LOC: 10.RF5
Procedural Knowledge
Easy
LOC: 10.RF5
Procedural Knowledge
Easy
LOC: 10.RF8
Conceptual Understanding
Easy
LOC: 10.RF8
Conceptual Understanding
Easy
LOC: 10.RF5
Conceptual Understanding
Easy
LOC: 10.RF8
Conceptual Understanding
Easy
LOC: 10.RF8
Conceptual Understanding
Easy
LOC: 10.RF3
Procedural Knowledge
Easy
LOC: 10.RF8
Conceptual Understanding
SHORT ANSWER
67. ANS:
{(Car #1, 3), (Car #2, 2), (Car #3, 5), (Car #4, 1)}
PTS: 1
DIF: Easy
REF: 5.1 Representing Relations
LOC: 10.RF4
TOP: Relations and Functions
KEY: Conceptual Understanding | Procedural Knowledge
68. ANS:
Lengths of Gam e Pieces
12
11
10
Length (cm)
9
8
7
6
5
4
3
2
Blue
White
Green
Yellow
Black
0
Red
1
Colour
PTS: 1
DIF: Moderate
REF: 5.1 Representing Relations
LOC: 10.RF4
TOP: Relations and Functions
KEY: Conceptual Understanding | Procedural Knowledge
69. ANS:
Hockey Player
Heritage
Jordin Tootoo
Inuit
Jonathan Cheechoo
Moose Cree
Sheldon Souray
Metis
Wade Redden
Metis
Chris Simon
Ojibwa
Sandy McCarthy
Mi’kmaq
PTS: 1
DIF: Moderate
REF: 5.1 Representing Relations
LOC: 10.RF4
TOP: Relations and Functions
KEY: Conceptual Understanding | Procedural Knowledge
70. ANS:
Sample answers
a)
b)
PTS: 1
LOC: 10.RF2
71. ANS:
domain:
range: {2 520}
PTS: 1
DIF: Moderate
REF: 5.2 Properties of Functions
TOP: Relations and Functions
KEY: Conceptual Understanding
DIF: Moderate
REF: 5.2 Properties of Functions
LOC: 10.RF1
72. ANS:
a) About 19 L
b) 45 min
TOP: Relations and Functions
KEY: Conceptual Understanding
PTS: 1
LOC: 10.RF1
73. ANS:
a) 4 s
b) 10 s
DIF: Moderate
REF: 5.3 Interpreting and Sketching Graphs
TOP: Relations and Functions
KEY: Conceptual Understanding
PTS: 1
LOC: 10.RF1
74. ANS:
a) 10 km
b) 115 min
DIF: Moderate
REF: 5.3 Interpreting and Sketching Graphs
TOP: Relations and Functions
KEY: Conceptual Understanding
PTS: 1
DIF: Moderate
REF: 5.3 Interpreting and Sketching Graphs
LOC: 10.RF1
TOP: Relations and Functions
KEY: Conceptual Understanding
75. ANS:
Segment EF is horizontal, so the volume of gas in the tank is constant. The car is stopped for 1 h.
PTS: 1
DIF: Moderate
REF: 5.3 Interpreting and Sketching Graphs
LOC: 10.RF1
TOP: Relations and Functions
KEY: Conceptual Understanding
76. ANS:
For each number in the first column, there is only one number in the second column. So, the relation is a
function.
PTS: 1
DIF: Easy
REF: 5.4 Graphing Data
LOC: 10.RF2
TOP: Relations and Functions
KEY: Communication | Conceptual Understanding
77. ANS:
a) The points on the graph should not be connected.
b) The points on the graph should be connected.
c) The points on the graph should be connected.
d) The points on the graph should not be connected.
PTS: 1
DIF: Moderate
REF: 5.5 Graphs of Relations and Functions
LOC: 10.RF1
TOP: Relations and Functions
KEY: Conceptual Understanding
78. ANS:
a) When the domain value is –2, the range value is 2.
b) When the range value is –1, the domain value is 4.
PTS: 1
LOC: 10.RF8
79. ANS:
Domain:
Range:
PTS: 1
DIF: Moderate
REF: 5.5 Graphs of Relations and Functions
TOP: Relations and Functions
KEY: Conceptual Understanding
DIF: Moderate
REF: 5.5 Graphs of Relations and Functions
LOC: 10.RF1
80. ANS:
TOP: Relations and Functions
KEY: Conceptual Understanding
PTS: 1
DIF: Moderate
REF: 5.6 Properties of Linear Functions
LOC: 10.RF4
TOP: Relations and Functions
KEY: Procedural Knowledge
81. ANS:
The relations in parts a, c, and f are linear.
PTS: 1
DIF: Moderate
REF: 5.6 Properties of Linear Functions
LOC: 10.RF4
TOP: Relations and Functions
KEY: Conceptual Understanding
82. ANS:
approximately 1.6 km/mi.
PTS: 1
DIF: Moderate
REF: 5.6 Properties of Linear Functions
LOC: 10.RF3
TOP: Relations and Functions
KEY: Procedural Knowledge
83. ANS:
i) Graphs b and d have a negative rate of change.
ii) Graphs a and e have a positive rate of change.
iii) Graphs c and f have neither a negative nor a positive rate of change.
PTS: 1
DIF: Moderate
REF: 5.6 Properties of Linear Functions
LOC: 10.RF4
TOP: Relations and Functions
KEY: Conceptual Understanding
84. ANS:
The independent variable is the number of quarters, n.
The dependent variable is the mass, m.
PTS: 1
LOC: 10.RF4
85. ANS:
Domain:
Range:
DIF: Easy
REF: 5.6 Properties of Linear Functions
TOP: Relations and Functions
KEY: Conceptual Understanding
PTS: 1
DIF: Moderate
REF: 5.7 Interpreting Graphs of Linear Functions
LOC: 10.RF5
TOP: Relations and Functions
KEY: Conceptual Understanding
86. ANS:
Horizontal intercept: 3
Vertical intercept: 2
PTS: 1
DIF: Easy
REF: 5.7 Interpreting Graphs of Linear Functions
LOC: 10.RF5
TOP: Relations and Functions
KEY: Conceptual Understanding
87. ANS:
Rate of change: 1; vertical intercept: 2
PTS: 1
LOC: 10.RF5
PROBLEM
DIF: Easy
REF: 5.7 Interpreting Graphs of Linear Functions
TOP: Relations and Functions
KEY: Procedural Knowledge
88. ANS:
a) {(81, 9), (90, 10), (99, 11), (108, 12), (117,13)}
b) Yes, the order of the numbers in each ordered pair does matter. The statement “81 divided by 9 is 9” is
true. However, if the numbers in each ordered pair were reversed, the statement “9 divided by 9 is 81”is
not true.
PTS: 1
DIF: Moderate
REF: 5.1 Representing Relations
LOC: 10.RF4
TOP: Relations and Functions
KEY: Communication | Problem-Solving Skills
89. ANS:
a) The total cost of the banquet is a function of the number of people attending. In function notation:
b) To determine C(46), use:
Substitute: g = 46
C(46) is the value of C when
.
This means that when 46 people attend the banquet, the total cost is $756.
c) To determine the value of g when
Substitute:
means that when
, use:
,
; that is, when 121 people attend the banquet, the total
cost is $1581.
PTS: 1
DIF: Difficult
REF: 5.2 Properties of Functions
LOC: 10.RF2
TOP: Relations and Functions
KEY: Communication | Problem-Solving Skills
90. ANS:
a)
b)
Value of Gas
Purchase, v
($)
1
2
12
20
40
50
Value of
Coupons, c
($)
0.03
0.06
0.36
0.60
1.20
1.50
c) To determine c(80), use:
c(80) is the value of c when
.
This means that when a customer spends $80 on gasoline, she will receive coupons valued at $2.40.
d) To determine the value of v when
, use:
means that when
,
gasoline to receive $5.00 in coupons.
; that is, a customer has to spend $166.67 on
PTS: 1
DIF: Difficult
REF: 5.2 Properties of Functions
LOC: 10.RF8
TOP: Relations and Functions
KEY: Problem-Solving Skills
91. ANS:
Segment FG: The volume of water in the bottle decreases from 1.25 L to about 0.1 L. This shows that
Katherine either drank, spilled, or poured out most of the water in her bottle.
Segment HI: The volume of water in the bottle increases from about 0.1 L to 2 L. This shows that Katherine
filled her bottle with water.
Segment KL: The volume of water in the bottle stays the same. This shows that Katherine did not drink any
water from her bottle during this time.
PTS: 1
DIF: Moderate
REF: 5.3 Interpreting and Sketching Graphs
LOC: 10.RF1
TOP: Relations and Functions
KEY: Communication | Problem-Solving Skills
92. ANS:
Oven Tem perature over Tim e
220
200
180
A
B
E
Temperature (°C)
160
F
140
120
100
80
60
40
20
C
O
20
40
60
D
80
100
Tim e (m in)
G
120
140
160
180
Segment OA: The temperature of the oven increases from 20 C to 190 C, so the segment goes up to the right.
Segment AB: A cake bakes for 30 min. The temperature does not change, so the segment is horizontal.
Segment BC: The temperature of the oven decreases from 190 C to 20 C, so the segment goes down to the
right.
Segment CD: The oven is turned off for 45 min. The temperature does not change, so the segment is
horizontal.
Segment DE: The temperature of the oven increases from 20 C to 160 C, so the segment goes up to the right.
Segment EF: The cookies bake for 20 min. The temperature does not change, so the segment is horizontal.
Segment FG: The temperature of the oven decreases from 160 C to 20 C, so the segment goes down to the
right.
PTS: 1
DIF: Difficult
REF: 5.3 Interpreting and Sketching Graphs
LOC: 10.RF1
TOP: Relations and Functions
KEY: Communication | Problem-Solving Skills
93. ANS:
a)
Segment
OA
AB
BC
CD
DE
EF
FG
Graph
The graph goes up to the right, so as
time increases, the distance from
Vancouver increases.
The graph is horizontal, so as time
increases, the distance stays the same.
The graph goes up to the right, so as
time increases, the distance increases.
The graph is horizontal, so as time
increases, the distance stays the same.
The graph goes down to the right, so
as time increases, the distance
decreases.
The graph is horizontal, so as time
increases, the distance stays the same.
The graph goes down to the right, so
as time increases, the distance
decreases.
Journey
In the first hour, the car leaves
Vancouver and travels approximately
105 km toward Hope.
The car stops for approximately 20 min.
The car travels approximately 45 km
toward Hope.
At C, the car has travelled 150 km so it
has reached Hope, where it stops for
2.25 h.
The car leaves Hope and travels
approximately 80 km toward
Vancouver.
The car stops for approximately 30 min.
The car returns to Vancouver.
b) The day trip was approximately 6.6 h.
c) The dependent variable is distance. The independent variable is time.
PTS: 1
DIF: Difficult
REF: 5.3 Interpreting and Sketching Graphs
LOC: 10.RF1
TOP: Relations and Functions
KEY: Communication | Problem-Solving Skills
94. ANS:
a)
Cost as a Function of Tim e
4
Cost ($)
3
2
1
30
60
90
120
Num ber of people
The points are not joined because the data are only valid for whole numbers of people.
b) The relation is a function because there is only one cost for each number of people.
PTS: 1
DIF: Moderate
REF: 5.4 Graphing Data
LOC: 10.RF1
TOP: Relations and Functions
KEY: Communication | Problem-Solving Skills
95. ANS:
Water in a Tub
Volume (L)
40
30
20
10
60
120
180
240
300
Tim e (s)
The points are joined because time and volume can have any numerical value between those indicated by the
points on the graph.
PTS: 1
DIF: Moderate
REF: 5.4 Graphing Data
LOC: 10.RF1
TOP: Relations and Functions
KEY: Communication | Problem-Solving Skills
96. ANS:
a)
0
4
8
12
16
Volume of Paint, p (L)
Cost, c ($)
Area Covered, A (m2)
0
0
52
37
104
74
156
111
208
148
b)
A
160
Area Covered by Paint
Area covered (m 2)
140
120
100
80
60
40
20
0
4
8
12
16
Volum e of paint (L)
p
Area that Can Be
Covered for a Given Cost
c)
A
160
Area covered (m 2)
140
120
100
80
60
40
20
0
d) Part b: domain:
Part c: domain:
50
100
150
Cost ($)
200
c
; range:
; range:
PTS: 1
DIF: Difficult
REF: 5.5 Graphs of Relations and Functions
LOC: 10.RF1
TOP: Relations and Functions
KEY: Communication | Problem-Solving Skills
97. ANS:
a) The points on the graph should be connected because all values of time and volume are permissible
between the indicated plotted points.
b) Domain:
PTS: 1
LOC: 10.RF1
; range:
DIF: Easy
REF: 5.5 Graphs of Relations and Functions
TOP: Relations and Functions
KEY: Communication | Problem-Solving Skills
98. ANS:
a)
To determine the value of f(x) when
Begin at
:
y
4
on the x-axis.
Draw a vertical line to the graph, then a
horizontal line to the y-axis.
The line appears to intersect the y-axis
at 5.
f(x) = 2 x +1
–4
–2
2
0
2
4
x
–2
So,
–4
When the domain value is 2, the range
value is 5.
b)
To determine the value of x when
:
Since
y-axis.
, begin at
y
4
on the
2
Draw a horizontal line to the graph, then a
vertical line to the x-axis.
g(x) = 1 – 2x
–4
–2
0
2
4
x
–2
The line appears to intersect the x-axis
at –1.
So, when
–4
,
When the range value is 3, the domain
value is –1.
PTS: 1
DIF: Moderate
REF: 5.5 Graphs of Relations and Functions
LOC: 10.RF8
TOP: Relations and Functions
KEY: Communication | Problem-Solving Skills
99. ANS:
a)
c
Cost of Renting a Paddle Boat
240
200
Cost ($)
160
120
80
40
0
1
2
3
4
5
Num ber of days
6
7
n
b) This graph represents a linear relation because the points lie on a straight line.
c) Choose two points on the line. Calculate the change in each variable from one point to the other.
Change in cost:
Change in number of days: 7 days – 3 days = 4 days
Rate of change:
The rate of change represents the daily cost of renting a paddle boat, which is $29.00 per day.
PTS: 1
DIF: Moderate
REF: 5.6 Properties of Linear Functions
LOC: 10.RF4 | 10.RF3
TOP: Relations and Functions
KEY: Communication | Problem-Solving Skills
100. ANS:
a) The dependent variable is the cost, c. The independent variable is the number of copies, n.
b) No, Sohan did not calculate the rate of change correctly. Instead of dividing the change in the cost by the
change in the number of pamphlets, he divided the change in the number of pamphlets by the change in
the cost.
Rate of change:
$0.14/pamphlet
c) The rate of change represents the cost of printing each pamphlet after the machine has been set up. The
cost per pamphlet is 14¢.
PTS: 1
DIF: Moderate
REF: 5.6 Properties of Linear Functions
LOC: 10.RF4 | 10.RF3
TOP: Relations and Functions
KEY: Communication | Problem-Solving Skills
101. ANS:
a) The independent variable is the time. The dependent variable is the distance.
b) Calculate the change in each variable.
Time
(min)
0
20
40
60
80
Change in
Time
Distance from
Destination (mi.)
285
244
203
162
121
Change in Distance
from Destination
Since the changes in both variables are constant, the relation is linear.
c) Change in time: 80 min – 0 min = 80 min
Change in distance:
Rate of change:
The distance from the destination is decreasing at a rate of 2.05 mi./min.; that is, the speed of the
helicopter is 2.05 mi./min.
d) The distance remaining to the destination is 121 mi.
Let t be the remaining time in minutes.
It will take the helicopter approximately 59 more minutes to reach its destination.
PTS: 1
DIF: Difficult
REF: 5.6 Properties of Linear Functions
LOC: 10.RF4 | 10.RF3
TOP: Relations and Functions
KEY: Communication | Problem-Solving Skills
102. ANS:
Time
(s)
0
4
8
12
Change in
Time
Height (m)
Change in Height
3700
3614
3458
3257
There is a constant change of 4 in the 1st column, but the differences in the 2nd column are not constant. So,
the relation is not linear.
Time
(s)
18
24
30
Change in
Time
Height (m)
2909
2561
2213
Change in Height
36
1865
Since the changes in both variables are constant, the table of values represents a linear relation.
PTS: 1
DIF: Moderate
REF: 5.6 Properties of Linear Functions
LOC: 10.RF4
TOP: Relations and Functions
KEY: Communication | Problem-Solving Skills
103. ANS:
a) The vertical intercept is 0. The horizontal intercept is 0. The point where the graph intersects the axes has
coordinates (0, 0). This means that the amount of gas in a gas tank after 0 s is 0 L.
b) Choose two points on the line. Calculate the change in each variable from one point to the other.
Change in time:
Change in volume:
Rate of change:
The rate of change is positive so the volume is increasing with time.
Every second, 0.5 L of gas is added to the tank.
c) The domain is the set of possible values of the volume of gas:
The range is the set of possible values of the time:
d) To estimate how long will it take to fill a 45-L gas tank, use the graph.
From 45 on the v-axis, draw a vertical line to the graph, then a horizontal line to the t-axis. From the
graph, it will take approximately 23 s.
PTS: 1
DIF: Moderate
REF: 5.7 Interpreting Graphs of Linear Functions
LOC: 10.RF3 | 10.RF5 | 10.RF8
TOP: Relations and Functions
KEY: Communication | Problem-Solving Skills
104. ANS:
a) Choose two points on the line. Calculate the change in each variable from one point to the other.
Change in length of shadow:
Change in height of object:
Rate of change:
The rate of change is positive so the length of the shadow increases with the height of the object.
For every 1 m of height, the length of the shadow is 3 m.
b) To estimate the length of the shadow, use the graph.
From 13 on the h-axis, draw a vertical line to the graph, then a horizontal line to the l-axis. From the
graph, the length of the shadow will be about 39 m.
c) To estimate the height of the building, use the graph.
From 45 on the l-axis, draw a horizontal line to the graph, then a vertical line to the h-axis. From the
graph, the height of the building will be about 15 m.
PTS: 1
DIF: Moderate
REF: 5.7 Interpreting Graphs of Linear Functions
LOC: 10.RF3 | 10.RF8
TOP: Relations and Functions
KEY: Communication | Problem-Solving Skills
105. ANS:
Since the function is linear, its graph is a straight line.
Determine the y-intercept:
Determine the x-intercept:
When
,
When
,
Determine the coordinates of a third point on
the graph.
When
,
6
y
4
2
Plot the points (0, 2), (5, 0), and (10, –2),
then draw a line through them.
–2
0
2
4
6
8
10
x
–2
–4
–6
PTS: 1
DIF: Moderate
LOC: 10.RF1 | 10.RF3 | 10.RF8
REF: 5.7 Interpreting Graphs of Linear Functions
TOP: Relations and Functions
KEY: Problem-Solving Skills
106. ANS:
a) On the vertical axis, the point of intersection has coordinates (0, 9000). The vertical intercept is 9000. At
the start of the trip, the distance from Beijing to Edmonton is 9000 km. On the horizontal axis, the point
of intersection has coordinates (12, 0). The horizontal intercept is 12. It takes approximately 12 h to fly
from Beijing to Edmonton.
b) Choose two points on the line. Calculate the change in each variable from one point to the other.
Change in distance:
Change in time:
Rate of change:
The rate of change is negative so the distance is decreasing with time.
Every hour, the distance to Edmonton decreases by approximately 750 km.
c) The domain is the set of possible values of the time:
The range is the set of possible values of the distance:
d) To estimate the distance to Edmonton, use the graph.
From 5 on the t-axis, draw a vertical line to the graph, then a horizontal line to the d-axis. From the graph,
the distance to Edmonton is approximately 5250 km.
e) To estimate how many hours the plane has been flying, use the graph.
From 6500 on the d-axis, draw a horizontal line to the graph, then a vertical line to the t-axis. From the
graph, the number of hours the plane has been flying is approximately 3
h.
PTS: 1
DIF: Moderate
REF: 5.7 Interpreting Graphs of Linear Functions
LOC: 10.RF3 | 10.RF5 | 10.RF8
TOP: Relations and Functions
KEY: Communication | Problem-Solving Skills