phs algebra 2 chapter 02 - scasd.org ch 2...algebra 2 chapter 2 23 phs_algebra_2_chapter_02 4/7/06...

Answers for Lesson 2-1 Exercises

1. 2.

3. 4.

5. (–2, –2), (–1, 1), (1, 1), (1, 0), (3, 3), (3, –2);domain {–2, –1, 1, 3}, range {–2, 0, 1, 3}

6. (–2, 3), (0, 1), (2, –1), (3, –2); domain {–2, 0, 2, 3},range {–2, –1, 1, 3}

7. (–2, 0), (–1, 2), (0, 3), (1, 2), (2, 0); domain {–2, –1, 0, 1, 2},range {0, 2, 3}

8. 9.

10. 11.

12. not a function 13. function

14. function 15. function

16. function 17. not a function

domain range5

101520

5101520

domain range

1

0

� 12

12

5101112

domain

018

range�2�1

012

domain�27

�8�1

0

range�3�2�1

0

O1 2 3

xy

O�1 x

y1

�1

O 2 4

�2

x

y

2

O�2�4 x

y

�2

�4

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Algebra 2 Chapter 2 23

PHS_Algebra_2_Chapter_02 4/7/06 4:38 PM Page 23

Answers for Lesson 2-1 Exercises (cont.)

18. function 19. function

20. not a function 21. function

22. -7, -3, 4, 11 23. 13, 7, -3.5, -14

24. 4.5, 6.5, 10, 13.5 25. -2, -4, -7.5, -11

26. 21, 13, -1, -15 27. -13, -9, -2, 5

28. 29 , 17 , -3 , -24 29. - , - , ,

30. - , - , - , 0

31. y = , where y is the number of meters and x is thenumber of inches; <1.50 m

32. domain {2, 3, 4, 5}, range {4, 5, 6, 7}

33. domain {-4, -3, -2, -1}, range {1, 2, 3, 4}

34. domain , range

35. domain , range e212, 12 fe23

2, 12, 32, 52 fO 31

xy

1

�1

e22, 212, 12, 2 fe21

2, 0, 2 fO

�1 1 x

y

1

O�4 �2 x

y4

2

Ox

y

6

4

2

2 4

x39.37

74

72

92

113

34

136

236

23

23

13

13

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PHS_Algebra_2_Chapter_02 4/6/06 5:02 PM 4


36. domain {2, 4, 8}, range {4, 8, 16}; function

37. domain {-2, -1, 0, 9}, range {2, 5, 7}; not a function

38. domain {all real numbers}, range {y $ 0}; function

39. domain {-3.2 # x # 3.2}, range {-1 # y # 1}; not afunction

40. A 41. B 42. C

43. yes 44. no 45. no

46. v(s) = s3; 2460.375 cm3

47. v(r) = pr3; about 4849 cm3

48. No; since 2 in the domain maps to 1 and 4, it is not afunction.

49. Check students’ work.

50. -3 51. 52. -4x - 14

53. 7 54.

55. Yes; each x is paired with a unique y.

56. No; each positive x is paired with two y values.

57. Yes; each x is paired with a unique y.

58. Function; if the domain and range are interchanged, it is nota function because 6 would be paired with both 2.5 and 3.0.

59. Domain {all integers}, range {all even integers}; function,each integer pairs to a unique even integer.

60. Domain {all integers}, range {all integers}; function, eachinteger pairs with its opposite.

61. Domain {all integers}, range {all even integers}; not afunction, each nonzero integer pairs with a pos. and neg.even integer.

34

223

43

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1. 2. 3.

4. 5. 6.

7. 8.

9. a.

y = 0.23x

domain {x∆x $ 0}

range {y∆y $ 0}

b. x-intercept (0, 0), y-intercept (0, 0); when no miles havebeen driven, there is no cost.

c. 0.23 represents a cost of $.23 per mile driven.

O1 3 5

x

y2

O1

xy

�5

�7

O 1x

y

3

1

O1 x

y

�1 5

O 2x

y

6

4

2

O 1x

y

5

3

1

O 1x

y

1

O�2 2

x

y4

2

�2

�4

O2

x

y4

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10. a.

b. The x-intercept is the point that represents selling 1000caps and 0 sweatshirts in order to raise the $4500. The y-intercept represents selling 0 caps and 360 sweatshirts toraise the $4500.

11. -1 12. -2 13. 3

14. 15. 16. 1

17. undefined 18. 0 19.

20. 3x - y = -2 21. 22.

23. y = -2 24. x + y = 2 25. 5x - y = -2

26. y - 3 = -1(x + 10) 27.

28. 29.

30. y - 11 = 1(x - 7) 31.

32. -5 33. 34.

35. 36. 37. 0

38. y = -3x - 5 39.

O x

y8

4

2

�2

O1

xy

�1

�5

�7

y = 52 x 1 13

2

AB2A

B

212

32

y 2 9 = 275(x 2 1)

y 1 1 = 243(x 2 0)y 2 10 = 25

2(x 1 4)

y 2 0 = 54(x 2 1)

35x 1 y = 212

556x 2 y = 19

3

175

215

411

O 500Caps

Sw

eats

hir

ts

x

y

300200100

1000

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40. y = 10 41. x = 1

42. 43.

44. 45.

46. 47.

O 2x

y6

4

2

O 1 3x

y5

3

1

O1 3

xy

�1

�3

O 2 4 6x

y

6

4

2

O 1x

y

3

1

O1 3 5

xy

�1

�3

�5

Ox

y4

2

O�2 2x

y

8

6

4

2

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48. 49.

50.

51. 52. 53.

54. , (0, 4), (-6, 0) 55. -1, (0, 1000), (1000, 0)

56. -0.8, (0, 0.4), (0.5, 0) 57. 54, (0, -1),

58. undefined slope, no y-intercept, (-3, 0)

59. 0, (0, 0), all pts. on x-axis 60.

61. 62. -

63. 64.

65. 66.

67. y = 3x + 2 68. y = - x -

69. B

70. Vertical lines cannot be graphed by this method.

71. y = -1 72. y = 2x + 1

O1

x

y

3

1

xy

O1

1

12

32

y = 34x 1 32 7

10

752 5

13

AB, Q0, CBR, QC

A, 0RRS, Q0, 2T

SR, QTR, 0R

212, Q0, 25

2R, (25, 0)

Q 154, 0R

23

214

23

13

O�1 x

y

�1

O1 3

xy

�1O1

xy

1

�1

�3

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PHS_Algebra_2_Chapter_02 4/18/06 7:41 AM Page 29


73. y = x + 74. y = - x - 1

75. 3x - 2y = 2 76. 9x + 3y = 2

77. 3x + 12y = -4

78. a–e. Check students’ work. The polygon is a rectangle.

79. yes 80. no

81. y = 3x + 6; y = - x + ;

82. The equation of the line connecting (1, 3) to (-2, 6) is y = -x + 4. The equation of the line connecting (1, 3) to (3, 5) is y = x + 2. The slopes are negative reciprocals so thelines are perpendicular. Therefore by def. of a right triangleit is a right triangle.

83. The slope of the line connecting (2, 5) to (4, 8) is , (2, 5) to(5, 3) is , (4, 8) to (7, 6) is , and (5, 3) to (7, 6) is . Sincethe adjacent sides’ slopes are negative reciprocals they areperpendicular. By the def. of a rectangle, it is a rectangle.

84. p: y = 4x + 16

q:

r: y = 4

O�1x

y

1

y � � x � 14 13

4

y �

4x

� 1

6

y � 4

y = 214x 1 13

4

3222

3223

32

Q12, 21

2R83

13

O�2 x

y4

2

32

O24x

y4

2

103

56

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1. yes; k = 2, y = 2x 2. yes; k = -3, y = -3x

3. no 4. yes;

5. yes; k = 7, y = 7x 6. no

7. yes; k = -2, y = -2x 8. no

9. yes; k = 12 10. yes; k = 6

11. yes; k = -2 12. no

13. no 14. yes; k = -5

15. yes; k = 6 16. no

17. 18.

19. k = -1; 5 20. k = 2; -10

21. 21 22.

23. a. 24. -3

b. 25. 4

c. <23 ft 1 in. 26. 10.5

27. 28. yes;

29. no 30. no

31. yes; k = 1.3, y = 1.3x 32. 682

33. y = 2x 34. 35.

36. y = -500x 37. 38.

39. 40. 41. 9

42. 6 43. 90 44. -140

45. 1.2

46. No; y = 1.7x does not contain the point (9, -9).

y = 2143 xy = 2

7x

y = 219xy = 3

5x

y = 292xy = 7

3x

k = 23, y = 2

3x53

s = 1336h

k = 1336

k = 214; 11

414k = 217

4 ;

k = 253; 25

3k = 27; 210

7

k = 13, y = 1

3x©

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47. Yes; y = - x contains the point (15, -12 ).

48. Yes; y = x contains the point (6 , 22 ).

49. Answers may vary. Sample:

50. Answers may vary. Sample: y = 3.2x

51. Answers may vary. Sample:

52. a. y = 28x b. 103.6 mi

c. 417.9 gal d. $.056/mi

53. Answers may vary. Sample: No; y = 0 passes through theorigin, but is not a direct variation.

54. Answers may vary. Sample: If y varies directly with x2,and y = 2 when x = 4, then when x = 9.

55. y is doubled. 56. y is halved.

57. y is divided by 7. 58. y is multiplied by 10.

59. a.

b. 32

c. z = kxy, x = k1w, so z = kk1wy, z varies jointly with w and y.

12

y = 1018

O xy

1

�1

y = 234x

O x

y

1

1

x

y1

�11

y = 0.5x

34

12

72

12

56

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1. d = 62.5h + 15

2. a. y = -50t + 1000

b. The y-intercept (0, 1000) represents thefilled pool, and the t-intercept (20, 0)represents the time needed to emptythe pool.

3. h = 8x + 60

4. y = x - 1; 5 leaves

5. y = 0.5x + 0.75; 3.25 lb

6. y = 58. x - 3. ; 172 blades of grass

7. y = 1.75x + 1.75; $8.40

8. Linear model is reasonable; modelsmay vary. Sample: y = -1.3x + 11

Ox

y

10

6

2

1 3 5 7 9

33

Years

Hei

gh

t(i

nch

es)

x

h90807060

1 2O

Ot

y1000

600

200

5Minutes

Gal

lon

s

15

h

d150

90

30

2O

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9. Linear model is reasonable;models may vary. Sample:y = 2.6x - 0.6

10. Linear model is reasonable; models may vary.Sample: y = -0.75x - 3.7

11. not reasonable

12. a. Linear model is reasonable.

b. 40

c. Answers may vary. Sample: After drawing a trend line onthe graph, locate the European size on the y-axis. Thenfind the corresponding U.S. size on the x-axis.

13. a. Answers may vary. Sample:y = 110x + 1170

b. 2930 Cal

c. Answers may vary. Sample:No; adults need fewerCalories, not more.

Age

Cal

ori

es

Ox

y3000

2000

1000

2 4 6 8 10121416

Ox

y50

30

10

2 4 6 8 10

�3�15

�9

O x

y

O10

y

�10

�10

x5

Ox

y25201510

5

1 3 5 7 9

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14. a.

b–e. Answers may vary. Samples are given.

b. c = 0.04A

c. The model fits the data very closely.

d. No; the area of the tarp is 150 ft2 so the price should be $6.00.

e. 6 3 8 ft; $0.07

15. y = -4x + 10 16. y = -3x - 6

17. y = -7.5x - 2.5 18. y = 1.4375x - 7.33125

19. a. y = 29.95 b. y = 2.95x; slope = 2.95, y-intercept = 0

c. Answers may vary. Sample:

Either way, you will average the same costs over the long run.

20. a. Answers may vary. Sample: y = 0.0714x - 9.3

b. 14.3 g

c. 200 Cal; a 200 Cal hamburger is closer to 5 g.

y

x

20

10

2 4Movies

Co

st (

$)

6 8 10O

y � 29.95

y � 2.

95x

OA

C70

50

30

10

100 300 500 700 900

Area (ft2)

Co

st (

$)

1100 1300 1500 1700



21. a. population

b–c.

d. 7 million

e. Answers may vary. Sample: Strong; the points fall close to a straight line.

22. D 23. 104.5 24. 85.8

25. 13

26. a.

b. about $2100

c. about $3400

d. Answers may vary. Sample: No, expenditure would bepredicted to be about $3600. The data point is far off theline.

1000 2000 3000 4000Ox

y5000

4000

3000

2000

1000

Per capita revenue ($)

Per

cap

ita

exp

end

itu

re (

$)

4 8 12 16 20Ox

y

12

8

4

Population (millions)

Lic

ense

d d

rive

rs(m

illio

ns)

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27. a.

b. y = -2x + 10

c. Answers may vary. Sample: neither; y = -1.5x + 12

28. y = 52x 2 2

y = 21711 x 1 14.27



1–9. Tables may vary. Samples are given.

1. 2.

3. 4.

5. 6.

7. 8.

x

y

O

5

3

1

1�1

�3

1 xyO

yx

5�2

1 13 3�1 10 2

yx

0�2�4 �4�2 �2

�1 10 2

x

y

O

3

1

1x

y

O

3

1

1

yx

5 2 0 1 4

23�1 10 2

yx

8 5 2 5 8�2 �1 0 1 2

x

y

O

3

1x

y

O

2

2

yx

6 3 0 3 6�2 �1 0 1 2

yx

5 1 0 3 7

14�1 0 1 2

yx

7 3 3 7�1

�1�2 0 1 2

x

y

O

5

3

1

yx 0

0 4 4 8 8�1 1 �2 2

x

y

O

5

3

1

1

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9. 10.

11. 12.

13. 14.

15. 16.

17. 18.

19. 20.

O x

6

2

�4

y �

3x

� 6y �

�3x �

6

O 1x

y

5

3

1

�3�5

y � x

� 6

y � �x � 6

O 1x

y

�1

1O xy

1

�1�2 2

O1x

y

1

�1

O xy

�11

O 1x

y1

O 1x

y

1

Ox

y

7

5

3

1

�1

O 2�2x

y4

2

�4�6

�1

�3

�5

xyO1�4

O�2�4 2 xy

�2

�4

52

yx

0�4�3 �5�1 �3

�3 �1� 0

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21. 22.

23. 24.

25. 26.

27. 28.

29. B 30. C 31. A 32. D

33. 34. 35.

Ox

y

3

1

1 3 5O x

y5

3

1

1

O1

x

y

3

1

O�2 2 x

6

4

2

yO�4�8

xy

�2

y � � x � 31

4 y � x � 114

Ox

y

6

4

2

2 4 6 8 10

y � � x � 8

12

y � x12

O 2 4 xy

�4

�6

6

y � x

� 8y �

�x � 4

O x

y5

1

y �

x

�9 2

3 2

y � �

x �92

32O�1 x

y

�2

2

1y �

2x �

1

y � �2x �

1

O2

y

�2

�4

4

y � x

� 5

y � �x � 5

Ox

y

3

1

1 3

y �

3x

� 6

y � �

3x � 6

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36. 37. 38.

39. 40. 41.

42. 43. 44.

45. 46. 47.

48. 49. 50. O1 3

xy

�1

O 1x

7

3

1

�3

O 1 x

y1

�3

1O xy

1

Ox

y6

4

2

2 4

O�2x

y2

O1�1 x

4

2

y

O

y

3

1

O�2�4 x

y

�2

O�2 x

4

2

�4

yO1 3 x

y

�1

�3

Ox

y7

5

3

1

1 3

O�2xy2

Ox

y

1

1O 1

xy

�3�5©

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51. A

52. a. b. Answers may vary. Sample:Same shape and size,different vertices, and onepoints down.

53. 54. 55.

56. 57. 58.

59. Answers may vary. Samples:

a. y = ∆x«, y = -∆x«

b. y = ∆x«, y = ∆x - 1« + 1

O�2 x

y

2

Ox

y4

2

2

Ox

y

5

3

1

1 3 5

O x

y2

2

O2

xy

�2O�2 2x

y2

�4 4 8 12�8�12O x

y

6

2

�2

�6

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1. 2.

3. 4.

5. 6. y = ∆x« + 4 7. y = ∆x« + 2

8. right 4 units 9. left 5 units

10. right 1 unit 11. left 2 units

12. y = ∆x + 2« 13. y = ∆x - 3« 14. y = ∆x - 4«

15. Answers may vary. Sample: 4.5 units left

16. Answers may vary. Sample: units to the right174

O x

y

�2

1

O x

y

2

2

�4 �2 O x

y4

2

Ox

y

3

1

1 3 5

y = u x u 2 23

O xy

�2 2

�4

�2

2�2 Ox

y4

2

O x

y

2

�2 2

4

6O

xy

�2

�2 2



17. 18. 19.

20. 21. 22.

23. y = 2∆x« 24. y = ∆x« 25. y = ∆x«

26. y = -2∆x« 27. y = - ∆x« 28. y = - ∆x«

29. vertical 30. combined 31. horizontal

32. combined 33. vertical 34. combined

35. y = ∆x - 2∆ - 2 36. y = -∆x - 1∆

O1 3 x

y

�1

�3

�5

5O�3�1

�3

xy

1 3O

xy

�2

1

�2 2

O�1 x

y1

O x

y

4

2

2 4

Ox

y

�2

1

�2 2

25

13

23

14

Ox

y

1

�5 �3O x

y

2

4

�2 2O

x

y

1

�2 2

Ox

y

1

4

2

Ox

y2

�3 2

Ox

y

3

1

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37. y = -∆x + 2« + 4

38. Horizontal; the graph is shifted left.

39. Answers may vary. Sample: Since a vert. translation affectsonly y-values and a horiz. translation affects only x-values,order is irrelevant.

40. a. c. y = 3x - 1

d. E

e. y = m(x - h) + k

b. y = 3x + 5

41. Check students’ work.

42. y = ∆x - 7« - 2 43. y = -∆x« - 3

44. y = -∆x + 5« 45. y = 2∆x + 4« + 3

46. y = ∆x - a« + b 47. y = -∆x - p« + q

48. 49.

4 right, 3 down6 right

50. 51.

3 left, 1 up3 right, 3 up

Ox

y

2

2y � ��x

� 1� � �

1

y � ��x � 2 � � � 2

O x

y3

1 3

y � ��x �

3 ��

y � ��x ��

1

Ox

y

1

1 3 5

y � ��x

� 4

��

y � ��x ��

3

O 2 4 6�2x

y

4

2

y � ��x

� 1

��

y � ��x �

5 ��

O�2

�2

xg

(x) �

3x

f (x

) � x

y

2

2

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52. a. b. Yes; Sample explanation;each t is paired with aunique height.

c. vertical translation 5 ft up

d. C

53. a. b.

c. d.

O x

y

�2

2

�2

2O 1�3 x

y

1

Oxy

�2

�2 2O

xy

1

�11

t

h(t)

Time

3

Hei

gh

t

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1. 2. 3.

4. 5. 6.

7. 8. 9.

10. a. y $ 20x if x # 6,y $ 15x if x . 6

b. Answers may vary. Sample:

11. 12. 13.

Ox

y

3

1

1 3 5O 2

x

y4

O 1x

y

1

Ox

y180

120

60

2 6Pounds

Min

ute

s

10Ox

y120

60

2

Min

ute

s

4Pounds

6

�1O

x

y3

1

1

O 2 xy

�2

�4

O 2x

y2

O 2x

y2

Ox

y

3

1

1 3 5

O 2 xy

�2

�4

xy

O 1�1

1

O

y

1

1xO

y3

1

1x

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14. 15.

16. 17.

18. 19.

20. y , -x - 2 21. 5x + 3y # 9 22. 2y $ ∆2x + 6«

23. 24. 25.

26. 27.

Ox

y

3

1

1 3 5 7 9 11O

x

y

5

3

1

1 3

y . 25x 1 2 Ox

y

2

2

O�5 �3 �1

1

x

y

O�1 x

y

1

O�2

�4

xy

2

Ox

y2

O x

y

6

4

2

2 4

O�4 �2

�2

xy

4

O�1x

y

63

�3

O x

y

4

2

2 4

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28. 29.

30. 31.

32. 33. 34.

35. Answers may vary. Sample: y # - x +

36. x . -3 37. y # x + 2

38. y $ -2x + 4 39. y # ∆x + 2«

40. y , -∆x - 4« 41. y . ∆x + 1« - 1

42. C

43. Answers may vary. Sample: when it lies on the boundary line

44. 45.

O�2 x

y4

2

�4

�2 2Ox

y2

32

953

53

2Ox

y

�2

4

2

4O x

y

�8

�16

�4

3Ox

y

�6

9

O5�5

x

y

2010

O�4 �2

�2

�4

�6

xy2 4 6

Ox

y

1

1

O

�1x

y1

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46. 47.

1 3 5Ox

y11

9

7

5

1

�2 2 4�4 Ox

y6

4

2

�2

�4

�6

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phs algebra 2 chapter 02 - scasd.org ch 2...algebra 2 chapter 2 23 phs_algebra_2_chapter_02 4/7/06...

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