Relations and Functions Class Work - NJCTLcontent.njctl.org/courses/math/algebra-i/alg...NJ Center for Teaching and Learning ~ 1 ~ Relations and Functions – Class Work Is the relation

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Relations and Functions – Class Work

Is the relation a function?

1. {(1,2), (3,4), (5,6)} 2. {(4,3), (3,2), (4,2)} 3. {(5,1), (3,1), (-4,1)}

4. 5. 6.

7. 8. 9.

10. 11.

12. 13.


Relations and Functions – Home Work

Is the relation a function?

14. {(3,1), (-2,6), (1,4)} 15. {(1,2), (2,2), (1,2)} 16. {(2,1), (5,1), (-6,7)}

17. 18. 19.

20. 21. 22.

23. 24.

25. 26.


Domain and Range – Class Work

Find the domain and range for each of the following

27. {(1,2), (3,4), (5,6)} 28. {(4,3), (3,2), (4,2)} 29. {(5,1), (3,1), (-4,1)}

30. 31. 32.

33. 34. 35.

36. 37.

38. 39.


Domain and Range – Home Work

Find the domain and range for each of the following

40. {(3,1), (-2,6), (1,4)} 41. {(1,2), (2,2), (1,2)} 42. {(2,1), (5,1), (-6,7)}

43. 44. 45.

46. 47. 48.

49. 50.

51. 52.


Evaluating Functions – Class Work

Let f(x) = 3x+4 and g(x) = |x-4|, find the following

53. f(2) 54. f(3) 55. g(6)

56. g(2) 57. 2f(6) 58. 0.5g(2)

59. f(4) – g(3) 60. g(5) – f(5) 61. f(0)2

62. g(3)3 63. g(a) 64. f(2b)

Evaluating Functions – Home Work

Let f(x) = (x-1)2 and g(x) = |2x-3|, find the following

65. f(2) 66. f(3) 67. g(6)

68. g(2) 69. 2f(6) 70. 0.5g(2)

71. f(4) – g(3) 72. g(5) – f(5) 73. f(0)2

74. g(3)3 75. g(a) 76. f(2b)


Explicit and Recursive Functions – Class Work

Write an explicit and recursive formula for the sequences below.

77. 12, 17, 22, 27, … 78. 3, 12, 48, 192, …

79. 128, 64, 32, 16, … 80. 59, 52, 45, 38, …

81. What is the recursive formula of f(n) = 11(5)n-1?

82. What is the explicit formula of f1 = 76 and f(n) = fn-1 – 3?

83. Write an explicit and recursive formula for the linear function, f(n) = 15x – 4.

Explicit and Recursive Functions – Class Work

Write an explicit and recursive formula for the sequences below.

84. 7, 21, 63, 189, … 85. 32, 38, 44, 50, …

86. 78, 65, 52, 39, … 87. 640, 160, 40, 10, …

88. What is the explicit formula of f1 = 2 and f(n) = 6∙fn-1?

89. What is the recursive formula of f(n) = 21 – 8(n-1)?

90. Write an explicit and recursive formula for the linear function, f(n) = 30 – 2x.


Multiple Representations of Functions – Class Work

91. What is the slope and y-intercept of the table? Write a function to represent the table.

92. A cell phone company charges $89.99 for a new phone and then $19.99 per month. Write a

function to represent this situation.

93. Write a function to represent the graph.

94. Joe was given $20 for his birthday. He then saved $10 per week from his allowance. Write a

function to represent this situation.

95. Which has the greater rate of change, the graph or the equation?

𝑦 = 2𝑥 + 1

x Y

-2 -4

-1 -1

0 2

1 5

2 8


96. Which has the greater rate of change, the table or the equation?

x -9 -6 -3 0 3 6 9

y -4 -3 -2 -1 0 1 2

y = -2x - 1

97. Which has the greater rate of change, the situation or the equation?

Stephanie climbs two steps at a time. y = -2x + 5

Multiple Representations of Functions – Homework

98. What is the slope and y-intercept of the table? Write a function to represent the table.

99. A plumber charges $75 for an initial house call and then $150 per hour. Write a function to

represent the situation.

100. Write a function to represent the graph.

X y

-2 -6

-1 -5

0 -4

1 -3

2 -2


101. Jillian purchased a car for $1500. After she drives it off of the lot, it begins to depreciate at a

rate of $120 per year. Write a function to represent the situation.

102. Which has the greater rate of change, the graph, the equation or the ordered pairs?

y = 6x + 4 (0,3) (3,6) (6,9) (12,12)

103. Which has the greater rate of change the situation or the ordered pairs?

The cost of going to the movies is $8 per person

(0,0) (1,7) (2,14) (3,21)


Functions Unit Review

Multiple Choice– Choose the correct answer for each question. No partial credit will be given.

1. Is the following a function?

a. yes b. no

2. Is the following a function? {(4,5) (4,-5) (2,1) (5,8)}

a. yes

b. no

3. Which numbers are NOT part of the domain. {(13,26) (15,30) (14,28) (11,22)} List all that apply.

a. 13

b. 26

c. 15

d. 22

4. Which numbers are NOT part of the range. {(13,26) (15,30) (14,28) (11,22)} List all that apply.

a. 11

b. 28

c. 15

d. 13

5. Find the domain of {(1,3), (5,6), (6,8)} a. {1, 5, 8} b. {1, 5, 6} c. {3, 6, 8} d. Set of Real Numbers

6. Find the range of f(x)= |x - 2| +3

a. [3, ∞] b. [1, ∞) c. (1, ∞) d. [3, ∞)

7. What is domain of the graph to the right?

a. -10< x< 10 b. -10< x< 10 c. -6< x< -2 or 0< x< 6 d. -10< x< -4 or -2< x< 4 or 6< x< 10

x 1 2 3 4 5

y 5 7 9 12 13


8. Which graph does NOT represent a function?

a. b. c. d.

9. Which graph does represent a function?

a. b. c. d.

Use for #’s 10 – 13, given f(x) = 2(x-6)2 +2 and g(x) = 3|x+4| 10. Find f(3)

a. 2 b. 20 c. 29 d. 38

11. Find g(-6)

a. 30 b. -6 c. -30 d. 6

12. Find f(5) – g(5)

a. -23 b. -27 c. 51 d. 23

13. Find f(2c)

a. 4c2 - 24c + 36 b. 4c2 - 24c + 38 c. 8c2 - 48c + 72 d. 8c2 – 48c + 74

In Questions 14 - 16, consider the following graph to the right: 14. The rate of change from x= 4 to x= 8 is

a. 3 b. 0.75 c. 0 d. -3


15. The greatest rate of change is between a. x= -7 and x= -6 b. x= -1 and x= 3 c. x= 1 and x= 2 d. x= 8 and x= 9

16. The rate of change from x= -5 to x= -4 is the same as the rate of change from

a. x= -6 to x= -5 b. x= -3 to x= -2 c. x= 6 to x= 7 d. x= 3 to x= 5

17. What is the explicit formula for the sequence below?

3, 15, 45, 225, …

a. a(n) = 3 + 5(n-1) b. a(n) = 5(3)n+1 c. a(n) = 3 + 5(n+1) d. a(n) = 3(5)n-1

18. What is the recursive formula for the sequence below?

3, 15, 45, 225, …

a. a1 = 3 and a(n) = 3(an-1) for n>1 b. a1 = 3 and a(n) = 5(an-1) for n>1 c. a1 = 3 and a(n) = 5(an-1) for n=1 d. a1 = 3 and a(n) = 3(an-1) for n=1

19. Write the recursive formula for the given explicit formula below.

f(n) = 7(4)n-1

a. f1 = 4 and f(n) = 7(fn-1) for n=1 b. f1 = 4 and f(n) = 7(fn-1) for n>1 c. f1 = 7 and f(n) = 4(fn-1) for n>1 d. f1 = 7 and f(n) = 4(fn-1) for n=1

20. In the table to the right, the rate of change between x= 4 and x= 6 is

a. 2 b. 1 c. 0.5 d. -1

Short Constructed Response – Write the correct answer for each question. No partial credit will be

given.

21. A cell phone company charges $30 a month and then $0.35 for any minutes over your plan. Write a

function to represent a monthly phone bill.


22. Which has the greater rate of change, the graph, the equation, or the ordered pairs?

(0,3), (3,6), (6,9), (9,12)

y = -3x + 7

23. Given f(x) = 2(1-x)3 and g(x) = 5x2, find f(4) + g(4)

Extended Constructed Response - Solve the problem, showing all work. Partial credit may be given.

24. Brenda decides to save her spare change in a jar. The initial amount in the jar, J(0), is $20, and after one week it is J(7)=23.50.

a. How much money did Brenda save?

b. At what rate is Brenda saving money?

c. If Brenda continued to save at a linear rate, how much would she have on J(14)? 25. The first term of a sequence is 4, the next term is six times the previous term.

a. What is the first five terms of the sequence?

b. Write a recursive function of the sequence.

c. Write an explicit function of the sequence.


26. Your parents are looking to rent a car for their upcoming vacation. They want your help in comparing the prices between two companies renting the same car. The first dealership called “Cars ‘R Us” charges an initial fee of $150 and then $99 a day. The second dealership called “Car Mart” charges an initial fee of $125 and then $115 a day.

a. What is the slope of the function for Car Mart? b. What is the y-intercept of the function for Cars ‘R Us? c. Fill in the table of values below. d. Explain which company is the better choice to use during your vacation

Day Cars ‘R Us Car Mart

1

2

3

4

5


Answers

Functions and Relations Class Work

1. Yes

2. Yes

3. Yes

4. Yes

5. Yes

6. No

7. No

8. No

9. Yes

10. No

11. Yes

12. Yes

13. Yes

Homework 14. Yes

15. No

16. Yes

17. Yes

18. No

19. No

20. Yes

21. No

22. No

23. Yes

24. No

25. Yes

26. Yes

Domain and Range Class Work

27. D: {1,3,5}, R: {2,4,6}

28. D: {3,4}, R: {2,3}

29. D: {-4,3,5}, R{1}

30. D: {-3,2,1}, R: {2,5,7}

31. D: {4,5,6}, R: {6}

32. D: {-4,0,2}, R: {3,4,5}

33. D: {-2,-1,2,3}, R: {0,3,4,5,7}

34. D: {1,2}, R: {3,4,5,6}

35. D: {-4,0,1,2,3}, R: {5,6,7}

36. D: {-4,-2,1,3}, R: {-3,-2,3,5}

37. D: [-4, ∞), R: [0, ∞)

38. D: (-∞,-2], R: [2, ∞)

39. D: all reals, R:[2, ∞)

Homework

40. D: {-2,3,1}, R: {1,4,6}

41. D: {1,2}, R: {2}

42. D: {-6,2,5}, R: {1,7}

43. D: {-1,0,1}, R: {6,7,8}

44. D: {2,4}, R: {6,7,8}

45. D: {-5,0,5}, R: {-2,-1,0}

46. D: {3,4,5,6}, R: {1,2,34}

47. D: {5}, R: {0,1,2,3}

48. D: {3,4}, R: {2,3,4}

49. D: {-4,-2,2,4,5}, R: {-3,2,4,5}

50. D: −6 ≤ 𝑥 ≤ 6, R: −6 ≤ 𝑦 ≤ 6

51. D: −8 ≤ 𝑥 ≤ 0, R: {-6,-2,2,6}

52. D: all reals, R: {2}

Evaluating Functions Class Work

53. 10

54. 13

55. 2

56. 2

57. 44

58. 1

59. 15

60. -18

61. 16

62. 1

63. |a – 4|

64. 6b + 4

Homework 65. 1

66. 4

67. 9

68. 1

69. 50

70. 0.5

71. 6

72. -9

73. 1

74. 27

75. |2a – 3|

76. (2b – 1)2

Explicit and Recursive Functions Class Work

77. a(n) = 12 + 5(n-1)

a1 = 12 and a(n) = an-1 + 5 for n>1

78. a(n) = 3(4)n-1


a1 = 3 and a(n) = 4 ∙ 𝑎𝑛−1,𝑛 > 1

79. a(n) = 128(1/2)n-1

a1 = 128 and a(n) = 1

2∙ 𝑎𝑛−1,𝑛 > 1

80. a(n) = 59 – 7(n-1)

a1 = 59 and a(n) = an-1 – 7, n>1

81. a1 = 11 and a(n) = 5 ∙ 𝑎𝑛−1,𝑛 > 1

82. a(n) = 76 – 3(n-1)

83. a(n) = -4 + 15(n-1)

a1 = -4 and a(n) = an-1+15,n>1

Homework 84. a(n) = 7(3)n-1

a1 = 7 and a(n) = 3 ∙ 𝑎𝑛−1,𝑛 > 1

85. a(n) = 32 + 6(n-1)

a1 = 32 and a(n) = an-1+6, n>1

86. a(n) = 78 – 13(n-1)

a1 = 78 and a(n) = an-1-13, n>1

87. a(n) = 640(1/4)n-1

a1 = 640 and a(n) = 1

4∙ 𝑎𝑛−1,𝑛 > 1

88. a(n) = 2(6)n-1

89. a1 = 21 and a(n) = an-1-8, n>1

90. a(n) = 30 – 2(n-1)

a1 = 30 and a(n) = an-1-2, n>1

Multiple Representations Class Work

91. m=3, b=2, f(x)=3x + 2

92. f(x)=19.99x + 89.99

93. f(x) = 2x + 5

94. f(x) = 10x + 20

95. Equation

96. Table

97. Situation

Homework 98. m=1,b=6, f(x) = 1x + 6

99. f(x) = 150x + 75

100. f(x) = 2x + 3

101. f(x) = -120x + 1500

102. Equation

103. Situation

Unit Review

1. A

2. B

3. B,D

4. A,C,D

5. B

6. D

7. D

8. D

9. C

10. B

11. D

12. A

13. D

14. B

15. B

16. A

17. D

18. B

19. C

20. C

21. f(x) = 0.35x+30

22. Equation

23. 134

24.

a. $3.50

b. $0.50/day

c. $27

25.

a. 4,24,144,864,5184

b. a1= 4 and a(n) = 6 ∙ 𝑎𝑛−1,𝑛 > 1

c. a(n) = 4(6)n-1

26.

a. m = 115

b. b = 150

c. see table below

d. Cars ‘R Us

Day Cars ‘R Us Car Mart

1 $249

$240

2 $348

$355

3 $447

$470

4 $546

$585

5 $645

$700


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Relations and Functions Class Work - NJCTLcontent.njctl.org/courses/math/algebra-i/alg...NJ Center for Teaching and Learning ~ 1 ~ Relations and Functions – Class Work Is the relation