Name: ________________________ Class: ___________________ Date: __________ ID: A

1

Unit 10 - Unit 6 Final Review - Functions

Multiple ChoiceIdentify 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.

a. {(House P, 1), (House Q, 3), (House R, 4), (House S, 5)}

b. {(3, House P), (4, House Q), (1, House R), (5, House S)}

c. {(1, House P), (3, House Q), (4, House R), (5, House S)}

d. {(House P, 3), (House Q, 4), (House R, 1), (House S, 5)}

____ 2. Canadian cities that currently have NHL hockey teams can be associated with the year in which they entered the league. Consider the relation represented by this table.

City Year of Entry

Calgary 1980

Edmonton 1979

Montreal 1917

Ottawa 1992

Toronto 1917

Vancouver 1970

Which ordered pair belongs to this relation?

a. (Toronto, 1917) c. (Ottawa, 1917)

b. (Edmonton, 1980) d. (Calgary, Alberta)

Name: ________________________ ID: A

2

____ 3. Which set of ordered pairs does not represent a function?

i) 2,5ÊËÁÁ ˆ

¯˜̃ , 3,8ÊËÁÁ ˆ

¯˜̃ , 4,11ÊËÁÁ ˆ

¯˜̃ , 2,−1ÊËÁÁ ˆ

¯˜̃

ÏÌÓÔÔÔÔ

¸˝˛ÔÔÔÔ

ii) 4,6ÊËÁÁ ˆ

¯˜̃ , 5,−7ÊËÁÁ ˆ

¯˜̃ , 7,9ÊËÁÁ ˆ

¯˜̃ , 8,−10ÊËÁÁ ˆ

¯˜̃

ÏÌÓÔÔÔÔ

¸˝˛ÔÔÔÔ

iii) −3,−8ÊËÁÁ ˆ

¯˜̃ , −1,−6ÊËÁÁ ˆ

¯˜̃ , −2,5ÊËÁÁ ˆ

¯˜̃ , 0,7ÊËÁÁ ˆ

¯˜̃

ÏÌÓÔÔÔÔ

¸˝˛ÔÔÔÔ

iv) 7,0ÊËÁÁ ˆ

¯˜̃ , 4,−1ÊËÁÁ ˆ

¯˜̃ , −6,5ÊËÁÁ ˆ

¯˜̃ , −8,0ÊËÁÁ ˆ

¯˜̃

ÏÌÓÔÔÔÔ

¸˝˛ÔÔÔÔ

a. i b. ii c. iv d. iii

____ 4. Identify the domain of this relation.

8,10ÊËÁÁ ˆ

¯˜̃ , 5,7ÊËÁÁ ˆ

¯˜̃ , 9,−11ÊËÁÁ ˆ

¯˜̃ , 6,−8ÊËÁÁ ˆ

¯˜̃

ÏÌÓÔÔÔÔ

¸˝˛ÔÔÔÔ

a. −8,7,9,10{ } c. 5,6,8,9{ }

b. −11,− 8,7,10{ } d. 5,6,9,10{ }

____ 5. Identify the range of this relation.

a. −2,3,5{ } c. −2,0,3,5{ }

b. 3,6,8{ } d. 1,3,6,8,9{ }

____ 6. This table shows the masses, m grams, of different numbers of identical beads, n. Identify the domain.

Number of Beads,n

Mass of Beads, m (g)

1 1.56

2 3.12

3 4.68

4 6.24

5 7.80

a. 1, 2, 3, 4, 5, 1.56, 3.12, 4.68, 6.24, 7.80{ }

b. 1, 2, 3, 4, 5, ...{ }

c. 1, 1.56, 2, 3.12, 3, 4.68, 4, 6.24, 5, 7.80, ...{ }

d. 1.56, 3.12, 4.68, 6.24, 7.80, ...{ }

Name: ________________________ ID: A

3

____ 7. This table shows the cost, C dollars, of different numbers of tickets sold, n. Identify the range.

Number of Tickets,n

Cost, C ($)

1 12.50

2 25.00

3 37.50

4 50.00

5 62.50

a. 1, 2, 3, 4, 5, ...{ }

b. 12.50, 25.00, 37.50, 50.00, 62.50, ...{ }

c. 1, 2, 3, 4, 5, 12.50, 25.00, 37.50, 50.00, 62.50{ }

d. 1, 12.50, 2, 25.00, 3, 37.50, 4, 50.00, 5, 62.50, ...{ }

____ 8. For the function f x( ) = −3x + 8, determine f(−2) .

a. 7 b. 2 c. 14 d. 3

____ 9. For the function f x( ) = −3x + 8, determine x when f x( ) = −25.

a. 83 b. –67 c. 11 d. –11

____ 10. For the function g x( ) = 2x − 9, determine g(3.4).

a. –2.2 b. 2.2 c. –3.6 d. 6.2

____ 11. For the function g x( ) = 2x − 9, determine x when g x( ) = −15.

a. –3 b. 12 c. –39 d. –12

____ 12. Write h x( ) = −3x + 2 as an equation in two variables.

a. x = −3h + 2 c. h = −3h + 2b. h = −3x + 2 d. x = −3x + 2

____ 13. Write y = 10x − 10 in function notation.

a. f x( ) = 10y − 10 c. f(y) = 10y − 10

b. f x( ) = 10x − 10 d. f(y) = 10x − 10

____ 14. Write g x( ) = −7x − 2.75 as an equation in two variables.

a. x = −7x − 2.75 c. g = −7g − 2.75

b. g = −7x − 2.75 d. x = −7g − 2.75

Name: ________________________ ID: A

4

____ 15. The function C fÊËÁÁ ˆ

¯˜̃ =

5

9f − 32Ê

ËÁÁ ˆ

¯˜̃ converts a temperature, f degrees Fahrenheit, to C degrees Celsius.

Determine C(39) to the nearest degree.

a. 38°C b. 102°C c. 4°C d. –4°C

____ 16. Identify the independent variable and the dependent variable for this table of values.

Hours Worked,h

Gross Pay, P ($)

4 38.00

5 47.50

9 85.50

20 190.00

30 285.00

a. independent variable: Pdependent variable: h

c. independent variable: gross paydependent variable: hours worked

b. independent variable: domaindependent variable: range

d. independent variable: hours workeddependent variable: gross pay

____ 17. Joshua went on a bike ride. Which statement best describes what is happening for line segment DE in this

graph?

a. Joshua spends time at the park.

b. Joshua leaves home.

c. Joshua cycles to the park.

d. Joshua returns home.

Name: ________________________ ID: A

5

____ 18. 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.

b. d.

____ 19. 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 c. $65/h

b. $110/h d. $90/h

____ 20. The monthly income, I dollars, of a furniture salesperson is given by the equation I = 0.03s + 1500, where s

represents the salesperson’s total monthly sales in dollars. Determine the rate of change of this linear relation.

a. 0.03 c. 1500

b. 33.3 d. 3

Name: ________________________ ID: A

6

____ 21. This graph shows the free-fall speed of a skydiver as a function of time. About how long did the skydiver’s

jump last?

a. About 20 s b. About 13 s c. About 60 s d. About 63 s

____ 22. This set of ordered pairs represents a linear relation. Determine its rate of change.

−6, 13ÊËÁÁ ˆ

¯˜̃ , 1, 10ÊËÁÁ ˆ

¯˜̃ , 8, 7ÊËÁÁ ˆ

¯˜̃ , 15, 4ÊËÁÁ ˆ

¯˜̃ , 22, 1ÊËÁÁ ˆ

¯˜̃

ÏÌÓÔÔÔÔ

¸˝˛ÔÔÔÔ

a.3

7c.

7

3

b. −7

3d. −

3

7

____ 23. The relation between x and y is linear. Which number would complete this table?

x 3 7 11 15 19

y 19 13 7 –5

a. –7 b. 1 c. –6 d. 6

____ 24. This table of values represents a linear relation. Determine the rate of change of the relation.

Time (s) 0 1 2 3 4

Distance (m) 0 5 10 15 20

a. 5 m/s b. 10 m/s c. 2 m/s d. 1 m/s

Name: ________________________ ID: A

7

____ 25. Which of these graphs represents a function?

i) ii)

iii) iv)

a. ii b. i c. iii d. iv

____ 26. Which situation represents a linear relation?

i) The number of cells decays at a rate of 12% each day.ii) A taxi company charges a $3 flat fee plus $1 for each kilometre travelled. iii) A population of bacteria doubles every hour for 6 h.iv) An investor’s portfolio increases in value by 6% each year.

a. i b. ii c. iii d. iv

____ 27. Which equation does not represent a linear relation?

i) y = x2

− 10

ii) x = −5 iii) y = −6x + 10

iv) 6x + 11y = 13

a. iii b. ii c. i d. iv

Name: ________________________ ID: A

8

____ 28. Which of these graphs represents a function?

i) ii)

iii) iv)

a. iv b. ii c. i d. iii

____ 29. Determine the domain and range of this graph.

a. 3 ≤ x ≤ 4; y ≤ −3 c. −3 ≥ x ≥ 4; y ≤ 3

b. x ≤ 3; − 3 ≤ y ≤ 4 d. −3 ≤ x ≤ 4; y ≤ 3

Name: ________________________ ID: A

9

____ 30. Determine the domain and range of the graph of this function.

a. 2 ≤ x ≤ 4; y ≤ 2 c. x ≤ 2; y ≤ 4

b. x ≤ 4; y ≤ 2 d. x ≤ 4; − 2 ≤ y ≤ 2

____ 31. This graph shows the cost of parking, c, as a function of time, t. Determine the domain of the graph.

a. 0.50,1.50,2.50,3.50,4.00{ } c. 30,45,75,90,120{ }

b. 1.00,1.50,2.50,3.00,4.00{ } d. 15,45,75,105,120{ }

____ 32. Which set of ordered pairs represents a linear relation?

i) (4, 9),(5, 7),(6, 5),(7, 3),(8, 1)ÏÌÓÔÔÔÔ

¸˝˛ÔÔÔÔ

ii) (5, 8),(6, 10),(7, 12),(8, 13),(9, 14)ÏÌÓÔÔÔÔ

¸˝˛ÔÔÔÔ

iii) (−1, 1),(0, 0),(1, 1),(2, 4),(3, 9)ÏÌÓÔÔÔÔ

¸˝˛ÔÔÔÔ

iv) (4, 6),(12, 5),(2, 4),(13, 3),(4, 2)ÏÌÓÔÔÔÔ

¸˝˛ÔÔÔÔ

a. iv c. ii

b. i d. iii

Name: ________________________ ID: A

10

____ 33. This graph shows the masses of people, m, as a function of age, a. Determine the range of the graph.

a. 4,5,8,12,14,17{ } c. 15,25,45,55,80,85{ }

b. 3,5,8,10,14,17{ } d. 20,25,45,65,80,85{ }

____ 34. This is a graph of the function g x( ) = −2x + 3. Determine the range value when the domain value is 2.

a. 0.5 b. 7 c. –1 d. 1

Name: ________________________ ID: A

11

____ 35. This is a graph of the function f x( ) = −2x − 4. Determine the domain value when the range value is –2.

a. 3 b. 1 c. 2 d. –1

____ 36. This graph shows the cost of hosting a dance, c, as a function of the number of students attending, n. What is

a restriction on the domain?

a. The domain can only contain positive numbers.

b. The domain can only contain whole numbers between 1000 and 3500.

c. The domain can only contain whole numbers.

d. The domain can only contain whole numbers that are multiples of 50.

Name: ________________________ ID: A

12

____ 37. 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?

a. The range can only contain negative numbers.

b. The range cannot contain negative numbers.

c. The range can only contain whole numbers up to 40.

d. The range can only contain whole numbers greater than 40.

____ 38. Determine the domain of this graph.

a. x > −5 c. −5 ≤ x ≤ 5b. x ≥ −5 d. y ≥ 2

Name: ________________________ ID: A

13

____ 39. Determine the range of the graph.

a. −1 ≤ y ≤ 0 c. −1 ≤ x ≤ 3

b. −4 ≤ y ≤ 0 d. −4 ≤ y ≤ 3

____ 40. Which table of values represents a linear relation?i)

Distance (m) 0 5 10 15 20

Time (s) 0 1 2 3 4

ii)

Time (s) 0 3 6 9 12

Distance (m) 0 10 22 36 52

iii)

Time (s) 0 1 2 3 4

Speed (m/s) 0 1 2 4 8

iv)

Distance (m) 0 4 16 36 64

Speed (m/s) 0 2 4 6 8

a. iii b. i c. ii d. iv

Name: ________________________ ID: A

14

____ 41. This graph represents a 150-L hot-water tank being filled at a constant rate. Determine the rate of change of

the relation.

a. 25 L/min c. 75 L/min

b. 3 L/min d. 0.33 L/min

____ 42. 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) 0 2 4 6 8

a (m) 4000 5400 6800 8200 9600

a. 1500 m/min b. 1400 m/min c. 1200 m/min d. 700 m/min

____ 43. 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.

a. $10 /CD c. −$10 /CD

b. −$20 /CD d. $14.29 /CD

Name: ________________________ ID: A

15

____ 44. The relation between x and y is linear. Which ordered pair completes this table of values?

x y

7 –4

4 –7

1 –10

–2 –13

a. (–5, –16) c. (–13, –5)

b. (–16, –5) d. (–5, –13)

____ 45. This graph shows distance, d kilometres, as a function of time, t minutes. Determine the vertical and horizontal intercepts.

a. Vertical intercept: 80

Horizontal intercept: 96

c. Vertical intercept: 96

Horizontal intercept: 80

b. Vertical intercept: 64

Horizontal intercept: 96

d. Vertical intercept: 80

Horizontal intercept: 64

Name: ________________________ ID: A

16

____ 46. This graph shows the volume of water remaining in a leaking hot tub as a function of time. Determine the

domain and range.

a. Domain: t ≤ 129Range: 0 ≤ V ≤ 1800

c. Domain: 0 ≤ t ≤ 129Range: V ≤ 1800

b. Domain: 0 ≤ V ≤ 1800Range: t ≤ 129

d. Domain: 0 ≤ t ≤ 129Range: 0 ≤ V ≤ 1800

____ 47. 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?

a. 45 min c. 50 min

b. 58 min d. 53 min

Name: ________________________ ID: A

17

____ 48. Which graph represents the linear function f x( ) = −3x + 4?

a. c.

b. d.

Name: ________________________ ID: A

18

____ 49. Which graph represents the linear function g x( ) = 4x − 1?

a. c.

b. d.

Name: ________________________ ID: A

19

____ 50. A retirement home ordered canvas shopping bags for 90 residents. This graph shows the cost of the shopping

bags, C dollars, as a function of the number ordered, n. Suppose one more shopping bag was ordered. What would be the increase in cost?

a. $0.25 c. $5.00

b. $4.56 d. $4.00

Short Answer

51. 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.

−8, 0, 4, − 6, 7, 0

52. For the function f x( ) = 4x − 7, determine f(−7.5).

53. For the function g x( ) = −2

3x + 5, determine x when g x( ) = 25.

54. a) Write in function notation: h = x − 2b) Write as an equation in two variables: k(x) = −4x − 1

Name: ________________________ ID: A

20

55. This graph shows how the volume of water in a barrel changes over time.

a) About how much water was in the barrel after 25 min?b) After how many minutes was the barrel empty?

56. Natasha spent part of the afternoon running errands. This graph shows her distance from home as a function of time.

a) How far did Natasha drive in total?b) How long was Natasha away from home?

Name: ________________________ ID: A

21

57. 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.

58. 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

Refund, r ($)

5 0.25

12 0.60

17 0.85

24 1.20

30 1.50

59. This table shows the refund, r dollars, for different numbers of pop cans, n. Write the domain and range.

Number of Pop Cans, n

Refund, r ($)

9 0.45

13 0.65

16 0.80

24 1.20

33 1.65

Name: ________________________ ID: A

22

60. Suppose you were to graph the data in this table of values. Would you join the points? Justify your answer.

Number of Pop Bottles, n

Refund, r ($)

5 1.00

12 2.40

17 3.40

24 4.80

30 6.00

61. How can you tell that this graph represents a function?

62. 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.

Name: ________________________ ID: A

23

63. This is a graph of the function h x( ) = −1

2x + 1.

a) Determine the range value when the domain value is –2.

b) Determine the domain value when the range value is –1.

64. Determine the domain and range of the graph of this function.

65. The set of ordered pairs below represents a linear relation. Determine the value of n.

−2, − 1ÊËÁÁ ˆ

¯˜̃ , 3.5, 10ÊËÁÁ ˆ

¯˜̃ , 9, 21ÊËÁÁ ˆ

¯˜̃ , n, 32ÊËÁÁ ˆ

¯˜̃ , 20, 43ÊËÁÁ ˆ

¯˜̃

ÏÌÓÔÔÔÔ

¸˝˛ÔÔÔÔ

66. Which equations represent linear relations? Create tables of values if necessary.

a) 5x − y = 8 d) y = x2

+ 29x − 30

b) x2

+ y2

= 11 e) y = x3

+ 8

c) x = 7 − 6y f) y − 5 = 0

Name: ________________________ ID: A

24

67. 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.) 9 18 27 36 45

Kilometres (km) 14.4 28.8 43.2 57.6 72.0

68. 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.

69. Determine the vertical and horizontal intercepts of this graph.

Name: ________________________ ID: A

25

70. Determine the rate of change and the vertical intercept of this graph.

71. Given the function f(x) = 3x − 1, find x when f(x) = 6.5

72. Given the function f(x) = 2x + 10, find x when f(x) = 11.5

73. Given the function f(x) = 2x + 10, find f(-1.75)

74. Given the functions f(x) = 4x + 2 and g(x) = −3x + 1, find x when g(x) = f(x)

Problem

75. 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.

Name: ________________________ ID: A

26

76. 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?

Number of People, n Cost, C($)

15 0.50

30 1.00

60 2.00

90 3.00

120 4.00

Name: ________________________ ID: A

27

77. Four litres of latex paint covers approximately 37 m2 and costs $52.

a) Copy and complete this table.

Volume of Paint, p (L) 0 4 8 12 16

Cost, c ($) 0 52

Area Covered, A (m2) 0 37

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.

Name: ________________________ ID: A

28

78. Sketch a graph of a function that has domain −3 ≤ x ≤ 1 and range −3 ≤ y ≤ 3.

Name: ________________________ ID: A

29

79. a) This is a graph of the function f x( ) = 2x + 1.

Determine the range value when the domain value is 2.

b) This is the graph of the function g x( ) = 1 − 2x .

Determine the range value when the domain value is 3.

Name: ________________________ ID: A

30

80. 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 Days (n)

Total Cost ($)

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.

81. Sketch a graph of the linear function f(x) = −2

5x + 2.

ID: A

1

Unit 10 - Unit 6 Final Review - FunctionsAnswer Section

MULTIPLE CHOICE

1. B

2. A

3. A

4. C

5. C

6. B

7. B

8. C

9. C

10. A

11. A

12. B

13. B

14. B

15. C

16. D

17. D

18. D

19. D

20. A

21. D

22. D

23. B

24. A

25. B

26. B

27. C

28. A

29. D

30. B

31. C

32. B

33. D

34. C

35. D

36. C

37. B

38. B

39. B

ID: A

2

40. B

41. B

42. D

43. C

44. A

45. A

46. D

47. D

48. A

49. A

50. D

SHORT ANSWER

51. Sample answers

a) −8,0ÊËÁÁ ˆ

¯˜̃ , 4,−6ÊËÁÁ ˆ

¯˜̃ , 7,0ÊËÁÁ ˆ

¯˜̃

ÏÌÓÔÔÔÔ

¸˝˛ÔÔÔÔ

b) 0, − 8ÊËÁÁ ˆ

¯˜̃ , 4,−6ÊËÁÁ ˆ

¯˜̃ , 0, 7ÊËÁÁ ˆ

¯˜̃

ÏÌÓÔÔÔÔ

¸˝˛ÔÔÔÔ

52. –37

53. –30

54. a) h(x) = x − 2

b) k = −4x − 1

55. a) About 19 L

b) 45 min

56. a) 10 kmb) 115 min

57. Segment EF is horizontal, so the volume of gas in the tank is constant. The car is stopped for 1 h.

58. For each number in the first column, there is only one number in the second column. So, the relation is a function.

59. The domain is: 9, 13, 16, 24, 33,…{ }

The range is: 0.45, 0.65, 0.80, 1.20, 1.65,…{ }

60. The points would not be joined because the data are only valid for whole numbers of pop bottles.

61. The graph represents a function because there is only one cost for each number of people.

62. 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.

63. a) When the domain value is –2, the range value is 2.

b) When the range value is –1, the domain value is 4.

64. Domain: x ≥ −4Range: y ≥ −3

65. 14.5

ID: A

3

66. The relations in parts a, c, and f are linear.

67. approximately 1.6 km/mi.

68. The independent variable is the number of quarters, n.The dependent variable is the mass, m.

69. Horizontal intercept: 3

Vertical intercept: 2

70. Rate of change: −1; vertical intercept: 2

71. x = 2.5

72. x = 0.75

73. 6.5

74. -1/7

PROBLEM

75. 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.

76. a)

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.

ID: A

4

77. a)

Volume of Paint, p (L) 0 4 8 12 16

Cost, c ($) 0 52 104 156 208

Area Covered, A (m2) 0 37 74 111 148

b)

c)

d) Part b: domain: 0 ≤ p ≤ 16; range: 0 ≤ A ≤ 148

Part c: domain: 0 ≤ c ≤ 208; range: 0 ≤ A ≤ 148

ID: A

5

78. There are many solutions to this problem. Any function that satisfies the restrictions on the domain and range

(as shown by the dotted lines) is acceptable.

Sample answer:

ID: A

6

79. a)

To determine the value of f(x) when x = 2:

Begin at x = 2 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.

So, f(2) = 5

When the domain value is 2, the range

value is 5.

b) To determine the value of x when

g(x) = 3:

Since y = g(x) , begin at y = 3 on the

y-axis.

Draw a horizontal line to the graph, then a vertical line to the x-axis.

The line appears to intersect the x-axis

at –1.

So, when g(x) = 3, x = −1

When the range value is 3, the domain

value is –1.

ID: A

7

80. a)

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: $228.00 − $112.00 = $116.00

Change in number of days: 7 days – 3 days = 4 days

Rate of change: $116.00

4 days= $29.00 / day

The rate of change represents the daily cost of renting a paddle boat, which is $29.00 per day.

ID: A

8

81. f(x) = −2

5x + 2

Since the function is linear, its graph is a straight line.Determine the y-intercept:When x = 0,

f(0) = −2

5(0) + 2

f(0) = 2

Determine the x-intercept:When f(x) = 0,

0 = −2

5x + 2

−2 = −2

5x + 2 − 2

−2 = −2

5x

x = 5

Determine the coordinates of a third point on the graph.When x = 10,

f(10) = −2

5(10) + 2

f(10) = −2

Plot the points (0, 2), (5, 0), and (10, –2),

then draw a line through them.