Answers to Algebra 2 Unit 1 Practice

[Pages:9]Answers to Algebra 2 Unit 1 Practice

Lesson 1-1

1. 65 5 15h 1 3

2. 4 hours; the cost of renting a bike for 4 hours is $63.

3. $13; it costs $78 to rent the bike for 5 hours since 15(5) 1 3 5 78. This is $13 more than Aaron has, 78 2 65 5 13.

4. B

5. a.No; there are 5 quarter-hour segments from 7:00 p.m. to 8:15 p.m. Using the equation c 5 40 1 4(5), c is $60.

b. Eliza should return the bike by 7:30 p.m. since 40 1 4(2) 5 48. She has enough money to keep the bike until 7:30 p.m.

10. No; sample answer: Substituting 15 for d in the equation and solving for c shows that Barbara does not have enough money to rent the bike for 15 days.

Lesson 1-3

11. a. x 5 210, x 5 24

210 28 26 24 22 0 2 4 6 8 10

b. x 5 6, x 5 7

210 28 26 24 22 0 2 4 6 8 10

c. x 5 2, x 5 10

Lesson 1-2

6. Number of Days Cost

1

$27

2

$47

3

$67

4

$87

5

$107

7. Sample answer: c 5 20d 1 7; c represents the cost of the bike rental, and d represents the number of days Susan rents the bike.

8.

c

125

100

Cost ($)

75

50

25

d 12345

Days

210 28 26 24 22 0 2 4 6 8 10

d. x 5 28, x 5 22

210 28 26 24 22 0 2 4 6 8 10

12. 48 # s # 62 13. a. 1 , x , 9

210 28 26 24 22 0 2 4 6 8 10

b. x # 24 1 or x $ 1 3

210 28 26 24 22 0 2 4 6 8 10

c. 24 3 # x # 5 1

4

4

210 28 26 24 22 0 2 4 6 8 10

d. x , 26 or x . 23

210 28 26 24 22 0 2 4 6 8 10

9. C

14. D 15. |w 2 2| # 8; 6 # w # 10;

210 28 26 24 22 0 2 4 6 8 10

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A1

SpringBoard Algebra 2, Unit 1 Practice

Lesson 2-1

16. y 5 3 x 1 2; 4

y

10 9 8 7 6 5 4 3 2 1

21029282726252423222211 22 23 24 25 26 27 28 29

210

x 1 2 3 4 5 6 7 8 9 10

17. B 18. f(e) 5 0.095e 1 1200

Monthly Earnings ($)

10,000 20,000 30,000 40,000 50,000

19.

f(e) Julian's Monthly Earnings

5000

4000

3000

2000

1000

e

Monthly Sales ($)

20. $8421.05; solve the equation 2000 5 0.095s 1 1200 for s.

Lesson 2-2

21. a.

y

10

9

8

7

6

5

4

3

2

1

x 21029282726252423222211 1 2 3 4 5 6 7 8 9 10

22

23

24

25

26

27

28

29

210

b. Dashed line; . means that points on the boundary line are not included in the solution set.

c. Above the line; (0, 0) is not a solution, so the half-plane that does not include (0, 0) should be shaded.

22.

y x , 2

10

9

y $ 23x 1 2 8 7 6

y # 2x

5

4

3

2

1

x 21029282726252423222211 1 2 3 4 5 6 7 8 9 10

22

23

24

25

26

27

28

29

210

23. C

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A2

SpringBoard Algebra 2, Unit 1 Practice

24. a. Sample answer: (22, 1) and (3, 6).

b. Sample answer: (22, 1) does not satisfy the constraint y $ 23x 1 2 and (3, 6) does not satisfy the constraint x , 2.

25. x $ 1, y , 2, y $ 1 x 2 2 2

Lesson 3-1

26. a. (1, 21)

y

10 9

8

7 6 5 4

3

2 1

21029282726252423222211 22 23 24 25 26 27 28 29

210

x 1 2 3 4 5 6 7 8 9 10

b. no solution

y

10 9

8 7 6 5 4

3

2 1

21029282726252423222211 22 23 24 25 26 27 28 29

210

x 1 2 3 4 5 6 7 8 9 10

c. (2, 0)

y

10 9 8 7 6 5 4 3

2 1

21029282726252423222211 22 23 24 25 26 27 28 29

210

x 1 2 3 4 5 6 7 8 9 10

d. infinitely many solutions

y

10 9

8 7 6 5 4

3 2 1

21029282726252423222211 22 23 24 25 26 27 28 29

210

x 1 2 3 4 5 6 7 8 9 10

27. a. (3, 1) b. (7, 2) c. infinitely many solutions d. (2, 5)

28. a. (4, 27) b. (4.5, 3) c. (2, 23) d. (10, 25)

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A3

SpringBoard Algebra 2, Unit 1 Practice

29. Sample answer: Multiply the first equation by 3 to

get

1.2x 1.2x

1 1.5 y 2 3.5y

5 7.5 5 2.5

.

Then

subtract

the

equation

to eliminate the variable x and get 5y 5 5.

30. C

39.

a.

29 216

23

2

b.

17

21

15

18 214 210

Lesson 3-2

31. a. (22, 4, 0)

b. (4, 3, 23)

( ) c. 24 , 27 , 4 77 d. (1, 5, 21)

32. a. (2, 23, 22)

( ) b.

1,

19 5

,

2

4 5

c. (23, 1, 5)

d. no solution

33.

a.

10c 6c

1 1

12 8f

f 1 3v 1 15v

5103.50 5125.50

12c 1 6 f 1 8v 5102.00

b. (3, 5, 4.5); A classic is $3, a fruit is $5, and a veggie is $4.50.

34. 4 pounds of peanuts, 2 pounds of cashews, and 4 pounds of raisins

35. B

Lesson 3-3

36. B 37. 3 3 3

32

3

38. a. 7 3 6

21 10 18

c.

4

9

9

14 10 0

23 5 3

1 24

13

b. 21 21 28

5 28 24

2

3

19

d. 6 6 214

3 213 221

c.

26 3

8 29

10

215

d. not defined

40. a. No. The matrices are not the same dimensions.

b. Yes. The number of rows in G is the same as the number of columns in H.

Lesson 3-4

41. B

42.

a.

21 22

1 1

x y

5

20 10

; (10, 30)

2

b.

3

3 3

1 1

x y

5

4 8

; (4, 1, 27)

2 4 1 z 5

43.

a.

x 1 y 5 5.5 7.95x 1 9.5y 5 47.6

b.

1 7.95

1 9.5

x y

5

5.5 47.6

c. (3, 2.5)

d. Lori bought 3 pounds of cheddar and 2.5 or 2 1

pounds of Swiss for the party.

2

55

44.

a.

12

17 10

33 13

p h

5

970 335

23 18 19 e 595

b. (10, 15, 5); During the sale, paperback books cost $10, hardcover books costs $15, and e-books cost $5.

45. Mari has 2 nickels, 5 dimes, and 35 quarters.

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Lesson 4-1

46. 23 # x , 12, [23, 12), {x | x , 23 # x , 12}

47. D A4

SpringBoard Algebra 2, Unit 1 Practice

48. a.

f (x)

b.

f (x)

10

10

9

9

8

8

7

7

6

6

5

5

4

4

3

3

2

2

1

1

x 21029282726252423222211 1 2 3 4 5 6 7 8 9 10

x 21029282726252423222211 1 2 3 4 5 6 7 8 9 10

22

22

23

23

24

24

25

25

26

26

27

27

28

28

29

29

210

210

domain: 2` , x , `, (2`, `), {x | x }; range: 2` , y # 2, (2`, 2], {y | y , y # 2}

domain: x fi 1, (2`, 1) and (1, `), {x | x , x fi 1}; range: 2` , y , 4, (2`, 4), {y | y , y , 4}

c.

f (x)

d.

f (x)

10

10

9

9

8

8

7

7

6

6

5

5

4

4

3

3

2

2

1

1

x 21029282726252423222211 1 2 3 4 5 6 7 8 9 10

x 21029282726252423222211 1 2 3 4 5 6 7 8 9 10

22

22

23

23

24

24

25

25

26

26

27

27

28

28

29

29

210

210

domain: 2` , x , `, (2`, `), {x | x }; range: 22 , y # `, (22, `), {y | y , y . 22}

49. (23) 5 211, (3) is undefined, (30) 5 895

domain: 2` , x , `, (2`, `), {x | x , x fi 21}; range: 25 , y , `, (25, `), {y | y , y . 5}

25

50. a. w(x) 5

0.01x 2 25 0.005x 1 50

0.0025x 1 112.5

if 0 , x # 5000 if 5000 , x # 15,000 if 15,000 , x # 25,000 if x . 25,000

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SpringBoard Algebra 2, Unit 1 Practice

b.

w(x) Water Charges

250

200

Cost ($)

150

100

50

x 10 20 30 40 50

Water (thousands of gallons)

c. Since the rate or charge for the water changes with the amount of consumption, the slope for each piece of the function is different.

d. $162.79; first determine the water consumption for a quarter of the year. Since there are 91.25 days in a quarter, the water consumption for a quarter is 247.2 gallons per day 3 91.25 days or 22,557 gallons. Next use the part of the piecewise function that corresponds to the range for the given number of gallons. Substituting 22,557 gallons for x in 0.0025x 1 112.5 5 $162.79.

Lesson 4-2

51. a.

f(x)

5

4

3

2

1

x 252423222211 1 2 3 4 5

22

23

24

25

b. f(2.4) 5 2, f(0.05) 5 0, f(23.6) 5 24

52. a.

h(x)

10

9

8

7

6

5

4

3

2

1

x 21029282726252423222211 1 2 3 4 5 6 7 8 9 10

22

23

24

25

26

27

28

29

210

b. domain: {x | x }; range: {y | y , y $ 0} c. (3, 0)

d.

f(x)

5

2x 1 3 x 2 3

if x , 3 if x $ 3

53. a. t(x) 5 45[x]

b.

t ( x)

225

Cost of Tutor

180

Cost ($)

135

90

45

x 12345

Hours

c. $90; $180 d. B

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A6

SpringBoard Algebra 2, Unit 1 Practice

54. a.

h(x)

5

4

3

2

1

x 252423222211 1 2 3 4 5

22

23

24

25

Lesson 5-1

61. a. x2 1 x 2 1

b. x2 2 x 1 3

c. x3 2 2x2 1 x 2 2

d.

x2 11 x22

,

x

fi

2

62. C

b. (0.3) 5 0, (3) is undefined, (1.1) 5 2, (100) 5 3

55. $392; no. A step function is a piecewise function with a constant value throughout each interval of its domain. The value of this function changes with each hour. It is a piecewise function because there are two different rates based on the number of hours worked.

Lesson 4-3

56. a. g(x) 5 2|x|

b. g (x) 5 1 x

3 c. g(x) 5 |x 2 5|

63. x 5 27, x 5 12; since both x2 2 5x and 84 are equal to (x), they are equal to each other. x2 2 5x 5 84. Now set the equation equal to 0 and solve the trinomial for x.

x2 2 5x 2 84 5 0 (x 1 7)(x 2 12) 5 0 (x 1 7) 5 0 or (x 2 12) 5 0 x 5 27 or x 5 12

64. a. m(x) 5 25,000 1 0.08x; p(x) 5 30,000 1 0.05x

b. The function (m 1 p)(x) represents the couple's total annual earnings.

c. (m 1 p)(x) 5 55,000 1 0.13x

d. g(x) 5 4|x| 1 2

e. g(x) 5 22|x 1 1| 2 3

57. domain: {x|x }; range: {y|y , y # 21} 58. f(x) 5 2|x 2 3| 1 1

59. C

60.

g(x)

d. the couple's annual earnings last year; $56,300

e. I could use (m 2 p)(x) to compare the annual earnings of Marty and his wife.

65. a.f(l ? w)(x) 5 (l 1 x)(w 1 x) 5 lw 1 lx 1 wx 1 x2

b. 527 sq ft

10 9 8 7 6 5 4 3 2 1

21029282726252423222211 22 23 24 25 26 27 28 29

210

x 1 2 3 4 5 6 7 8 9 10

Lesson 5-2

66. y(x(z)) 5 6z 23; 21

67. The domain of the composite function is the range of k(l), all real numbers greater than or equal to 22.

68. a. c(h) 5 15 1 75h

b. domain: hours, range: dollars

c. The slope is 75. It means the cost will increase by $75 for each additional hour of repair time.

69. a. (x) 5 0.75x b. c((x)) 5 15 1 75(0.75x) 5 15 1 56.25x

c. C

a vertical translation of 23, a horizontal translation of 21, and a vertical shrink by 1

2

70. The cost will not be the same; for each new location, you have to add the flat fee of $15.

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A7

SpringBoard Algebra 2, Unit 1 Practice

Lesson 5-3

71. a. 9 c. 16

72. a. 34 c. 23 e. 25 g. 2

73. a. 4x2 74. D 75. a. s(p) 5 0.75p

b. t(p) 5 1.07p c. $361.13

b. 11 d. 11 b. 23 d. 9 f. 215 h. 27 b. 2x2

Lesson 6-1

76. 15

77. a. f 21(x) 5 x 21 3

b. g21(x) 5 2x 1 6

c. h21(x) 5 4 x 1 4 3

d. j 21(x) 5 4x 2 3 2

78. B

79.

a.

k(15)

5

15 5

5

3;

the

map

distance

between

two

points that are actually 15 kilometers apart is

3 centimeters.

b. k21(a) 5 5a; the inverse function is the actual distance in kilometers between two points that are a centimeters apart on the map.

c. k21(3) 5 5 ? 3 5 15 kilometers 80. f21(8) 5 2

Lesson 6-2

81. a. f 21(x) 5 x 1 2 ; f 21( f (x)) 5 (3x 2 2) 1 2

3

3

5 3x 5 x 3

b.

g21(x)

5

3x

2

12;

g

21

(

g

(x

))

5

3

1 3

x

1

4

2

12

5 x 1 12 2 12 5 x

82. D

83. a.

y

10 9

f (x) f 21 (x)

8

7

6

5

4

3

2

1

x 21029282726252423222211 1 2 3 4 5 6 7 8 9 10

22

23

24

25

26

27

28

29

210

b.

y

f (x)

10

9

8

7

6

5

4

3

f 21 (x)

2

1

x 21029282726252423222211 1 2 3 4 5 6 7 8 9 10

22

23

24

25

26

27

28

29

210

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SpringBoard Algebra 2, Unit 1 Practice

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