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35

Chapter 5 Answers

Answers Algebra 1 Chapter 5

Practice 5-11. The student is traveling at a constant speed.2.

3. The distance from home is not changing.4. The distance from home decreases.5. The distance from home increases.6.

Answers may vary. Sample: In section 0 to 1, the hiker isascending. In section 1 to 2, the hiker’s elevation is constant. Insection 2 to 3, the hiker is descending.

7.

Answers may vary. Sample: In section 0 to 1, speed is increas-ing. In section 1 to 2, speed is constant. In section 2 to 3, speedis decreasing.8.

Answers may vary. Sample: Where the graph is increasing, theheight above the ground is increasing. Where the graph is flat,the height is not changing. Where the graph is decreasing, theheight above the ground is decreasing.

9.

Answers may vary. Sample: In sections 0 to 1, 3 to 4, and 6 to 7,the speed is increasing. In sections 2 to 3, 5 to 6, and 8 to 9, thespeed is decreasing. In sections 1 to 2, 4 to 5, and 7 to 8, thespeed is constant. At 0, 3, 6, and 9, the car is not moving.10.

11.

12.

Practice 5-21. d = {-3,-1, 0, 2, 4}; r = {-7,-3,-1, 3, 7}2. d = {-5,-4, 0, 1, 2}; r = {-4,-2, 2, 3, 4} 3. yes 4. no 5. yes 6. no 7. yes 8. no 9.-9 10. 0 11. 1 12. -2 13. 1.8 14. 1 15. -4 16. 1.25 17. 2.5 18. -1 19. {1, 4, 7} 20. {-2, 0} 21. {-9,-1}

22. 23a. d(t) = 60t 23b. {60, 300, 600}

23c. Domain is time and range is distance traveled.

e0, 12 f

Speed vs. Time

Time

Spee

d

0

Speed vs. Time

Time

Spee

d

0

Speed vs. Time

Time

Spee

d

0

Trip to Store

Time

Spee

d

10 2 3 4 5 6 7 8 9

Plane Trip

Time

Hei

ght

Abo

ve G

rou

nd

0

Trip to School

Time

Spee

d

0 1 2 3

Mountain Hike

Time

Ele

vati

on

0 1 2 3

Trip to School

Time

Spee

d

0

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36 Algebra 1 Chapter 5 Answers

Chapter 5 Answers (continued)

Practice 5-3For Exercises 1–11, answers may vary. Sample:

1.

2.

3.

4.

5.

6.

7.

8.

9.

10a.

10b. 231 mi 10c. Yes; g is continuous but it only makessense for positive values.

�30

102030

O

D(g)

1 2 3�2�1�3

g

g d(g)

0 0

1 22

2 44

�6

�2

42

4 6O x

f(x)

�2�4

x f(x)

-3 -6

0 -3

3 0

6 3

�1�2�3�4

1O

f(x)

1 2 3�2�3x

x f(x)

-2 -2

0 2

2 -2

3 -7

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O

f(x)

21 3�2�1�3x

x f(x)

-2 5

-1 2

0 1

1 2

2 5

�4�2

4

6O x

f(x)

�2�4

x f(x)

-3 3

0 1

3 -1

6 -3

21

2 3 41O x

f(x)

�1

x f(x)

-2 -1

0 0

2 1

4 2

42

68

4 62O x

f(x)x f(x)

0 -2

2 1

4 4

6 7

�2�1

234

1

1 2O x

f(x)

�1�2

x f(x)

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0 -2

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2 4

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21

1O x

f(x)

�1�2

x f(x)

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-1 -2

0 0

1 2

23

21O x

f(x)x f(x)

-1 0

0 1

1 2

2 3

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37

Chapter 5 Answers (continued)

Answers Algebra 1 Chapter 5

11a.

11b. $6.00 11c. No; n is a discrete variable.

12. 13.

14. 15.

16.

17.

18. 19.

20.

21. 22.

23.

For Exercises 24 – 26, answers may vary. Sample:24. 25.

26. x y

-2 2

-1 0

0 0

1 2

x y

0 2

1 -1

2 -4

x y

0 -1

1 1

2 3

O

2

�2

�2

2x

y

�6�8

�4�2

42

6

O42�4

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y

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3

56

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24

8

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2

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a2 14, 2 178 b

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38 Algebra 1 Chapter 5 Answers

Chapter 5 Answers (continued)

Practice 5-41. ƒ(x) = x + 3 2. ƒ(x) = 3x 3. ƒ(x) = x - 5 4a. C(p) = 0.39p 4b. $1.37 5a. C(n) = 50 + 10n5b. $110 6. ƒ(x) = 7. ƒ(x) = x2 8. ƒ(x) = 20 - x9a. N(b) = 12b 9b. 192 pens 10a. C(n) = 20 - 1.25n10b. $13.75 10c. no 11a. P(n) = 9.50a - 209 11b. $19.00 11c. 22 shirts

Practice 5-51. yes; 5 2. yes;-4 3. no 4. no 5. yes; 3 6. yes;

7. yes; 8. no 9. no 10. yes; 2 11. no 12. yes;13. 4 14. -3 15. 3 16. -3 17. 5 18. 3 19. -8 20. 12 21. 2 22. 4.5 23. 2.5 24. -6 25. yes; y = 2x26. yes; 27. no 28. yes; y = 1.4x 29a.29b. 350 mL 30a. g = 4c 30b. 96 31. $75

Practice 5-61. xy = 54 2. xy = 18 3. xy = 4. xy = 91 5. xy = 726. xy = 3.92 7. xy = 484 8. xy = 76 9. xy = 10 10. 1011. 8 12. 16 13. 2 14. 37 15. 625 16. 4 17. 18. 2

19. 3.6 20. 9.3 21. 2.3 22. 6 23. 3 24. 16 25. Inverse 26. Direct 27. Inverse variation; xy = 70 28. Inverse variation; xy = 48 29. Direct variation; y = 11x30. Direct variation; y = 4.5x 31. Inverse variation; xy = 3632. Direct variation; y = 2.1x 33. Direct variation; y = 6.4x34. Inverse variation; xy = 6 35. Inverse variation; xy = 1836a. 5 m3 36b. 2 atm 36c. 19.2 m3 37a. 1.5 h 37b. 192 ft/s

Practice 5-71. 6 2. -3 3. -5 4. 3 5. 6. 7. 1.5 8. -2.5 9. 1.1 10. 0.9 11. 2.4 12.-1.7 13. 25, 31 14. 4, 7 15. -19,-24 16. 17. 7.9, 9.2 18. -26.6,-35.7

19. 20. -4 ,-6 21. 44, 94, 994 22. -18,-58,-778 23. 31, 66, 696 24. -31,-46,-31625. 26. 2.7, 7.7, 97.7 27. 404, 909, 999928. -397,-892,-9802 29. 0.6,-4.9,-103.9

30. 31. yes; common diff. = -0.2

32. no 33. no 34. no 35a. $100, $135, $170, $205 35b. $35 35c. $240, $905, $1745, $2585

Reteaching 5-11. It shows total distance traveled. 2. It shows elapsed time.

3.

4. The flat part of the graph. When you are taking pictures,you are not moving. 5. The ride down Lookout Knoll. Whenyou ride down, you go faster and cover the distance in a shorter amount of time.6.

Reteaching 5-21. d = {-4,-2, 0, 1, 2}; r = {-1, 0, 3, 4, 6} 2. d = {-6,-3, 1, 2, 3}; r = {-4,-1, 2, 4, 7} 3. no 4. yes 5. -8 6. 6 7. -4 8. 5 9. 1 10. 5 11. {0, 4} 12. {-3, 0,-1} 13. {2, 3, 7} 14. {-2, 0, 4} 15. {4, 6} 16. {-7,-5}

Reteaching 5-31. 2.

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2x

y

O

2

�2

�2

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om B

ase

Photo Trip

uphilldownhill

taking photos

Time0

Tota

l Dis

tan

ce

Photo Trip

uphill

downhill

taking photos

downhill

2412, 253

4, 22814

274, 217

4 , 21974

14

122

13, 22

272, 29

2

212

12

625

13

16

V 556Ty 5

23x

295

32

35

12x

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39Answers Algebra 1 Chapter 5

Chapter 5 Answers (continued)

3. 4.

5. 6.

7. 8.

Reteaching 5-41. ƒ(x) = 3x 2. ƒ(x) = x - 1 3. ƒ(x) = x2

4. /(w) = 4w + 2 5. w(/) = / 6. c(a) = 0.99a

7. d(t) = 65t 8. v(q) = 0.25q 9. e(n) = 8.25n 10. f(d) = 3d

Reteaching 5-51. yes;-3 2. no 3. yes;-2 4. yes; 1 5. yes; 2 6. no

Reteaching 5-61. 151; 132 2. $10.22

3.

Reteaching 5-71. 7 2. -4 3. 11 4. -6,-8 5. 8, 11 6. -37,-42 7. A(n) = 2 + 7(n - 1); 30; 658. A(n) = 5 - 4(n - 1);-11;-31 9. A(n) = -52 + 11(n - 1);-8; 47

Enrichment 5-11–8. Answers will vary. Samples:1. the temperature during the day 2. a car accelerating, goingat a constant speed, decelerating, and then continuing at a con-stant speed 3. amount of an element undergoing decay 4. height of a growing child over the year 5. amount of moneyin an investment account compounded 6. height of a personwhen riding a ferris wheel 7. the closing prices of the stockmarket 8. the rate of postage to mail letters by the ounce

Enrichment 5-21. 0.3, 0.65, 0.1, 0.5; {(30, 0.3), (65, 0.65), (10, 0.1), (50, 0.5)} 2. yes;

3. 4. 0.15; 0.6; 1.8 5. 0.025; 0.4; 3.66. 0.45; 0.3; 0.1 7. 5.5; 10; 22 8. yes;

9. no, 6% is paired to two different values. 10. yes; each firstelement is paired only once.

Enrichment 5-31. 2.

O

2

�2

�2

2x

y

O

2

�2

�2

2x

y

O

20

40

60

62 4x

y

Hour

Perc

ent

f(x) 5x

100

O

0.2

0.4

0.6

6020 40x

y

Price No. Sold

$12.50 132

$12.00 138

$11.50 144

$11.00 151

$10.22 162

12

O

2

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�2

2x

y

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2x

y

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y

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4

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y

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3. 4.

5. 6.

7. 8.

9. 10.

11. 12.

13. 14.

15. 16.

17. decreases without bound, increases without bound18. increases without bound, decreases without bound19. approaches 0, increases without bound20. increases without bound, approaches 021. decreases without bound, increases without bound22. approaches 0, increases without bound

Enrichment 5-41. 2. 72 3. 3.5 4. 4 5. 4, 4, 4 6. 225 7. 4.6 8. 3.8 9. p = i - e - t 10. $8000 11. $52,000 12. $3889

Enrichment 5-51. c 2. 30 c 3. 8 pies 4. 4 tbs (4 full pies)

5. 10; 5 c; tsp; 10 tbs; tsp 6. yes 7. no 8. yes

9. yes; 10. 32 oz; 1 c; 1 c; 4 tsp; tsp; 8 c; 32 oz

Enrichment 5-61. Answers may vary. Sample: (2, 10), (4, 5), (5, 4)

2. Answers may vary. Sample: ,

3. Yes; For every point, xy = -12 and xy = 12.4. Answers may vary. Sample:

, , , ;

for x . 0, for x . 0,

for x , 0, for x , 0

Enrichment 5-7Leonardo Fibonacci

Chapter ProjectActivity 1: DoingCheck students’ work.

Activity 2: GraphingCheck students’ work.

i(x) 5 212xh(x) 5

12x

g(x) 5 212xf(x) 5

12x

x i(x)-2 6-3 4-4 3

x h(x)-2 -6-3 -4-4 -3

x g(x)2 -63 -44 -3

x f(x)2 63 44 3

4510

2

rangedomain

45

x y2 104 55 4

12

21221

2

112

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2

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y

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40

Chapter 5 Answers (continued)

Algebra 1 Chapter 5 Answers

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41Answers Algebra 1 Chapter 5

Chapter 5 Answers (continued)

Activity 3: Writing21.5 s, the time it takes 5 people in a row to say the tonguetwister; It takes 0 people in a row 0 s to say the tongue twister;Solve 4.3n = 34.4 for n; Check students’ work.

Activity 4: AnalyzingCheck students’ work.

✔ Checkpoint Quiz 11.

2.

3.

4. No, the graph fails the Vertical Line Test.

5. -2 6. 7. 1 8. 9. -1 10.

✔ Checkpoint Quiz 2

1. ; ; 5

2. ;

3. ;

4. ; ; -3

5. A(t) = 7.75t 6. C(n) = 0.49n 7. 6 8. -14.6

9. 12 10. A(t) = 5.65t

Chapter Test, Form A1. Answers may vary. Sample:

Going up

Time0

Hei

ght

Down

Down

StoppedHeight of Elevator

O

2

�2

�2

2x

yx g(x)

-2 6

-1 3

0 0

1 -3

2 -6

O

2

�2

�2

2x

yx f(x)

-2 5

-1 3

0 1

1 -1

2 -3

O

2

�2

�2

2 x

y

O

4

�4

�4

4x

yx y

-2 -10

-1 -5

0 0

1 5

2 10

12

522

52

Time (hours)

Popu

lati

on

Time

Dis

tanc

e

Years

Hei

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Chapter 5 Answers (continued)

42 Algebra 1 Chapter 5 Answers

2. Answers may vary. Sample:

3. yes 4. no 5. If any x-coordinate occurs more than oncewith different y-coordinates, then the relation is not a function.6. {14, 8, 6, 3,-4} 7. {44,-1,-4, 2.75, 71}8. Answers may vary. Sample:

9. Answers may vary. Sample:

10. ƒ(x) = 35x 11. ƒ(x) = 5.50x 12. ƒ(x) = 5.00 - 0.89x

13. ƒ(x) = 2x + 1 14. 15. Answers willvary. Sample: The amount of change you would get fromspending a $10 bill. 16a. ƒ(x) = $13.50x 16b. $81.00

16c. 14h 17. 18. 19.

20. 21. yes; y = -4x 22. no 23. 36 24. 1625. -45.6 26. A relation is a function when each x-value ispaired with exactly one y-value. 27. 5.08 h 28. -4.5;-7,-11.5,-16 29. 3;-5,-2, 1 30. -9 31. 1.5 32. yes; the common difference is -2.2.33. no; there is no common difference

Chapter Test, Form B1.

2. Domain {1, 2, 3, 5}Range {5, 9, 11, 12}

3. Domain

Range

4. 5. ƒ(x) = x + 2 6. -38 7. 19

8. {10, 31, 38.5} 9. {-5, 4, 7, 16}10. Tables may vary. Sample:

11. Tables may vary. Sample:

12. ƒ(x) = 1.29x 13. ƒ(x) = 12x 14a. ƒ(x) = 1.65x

14b. $234.30 15. y = 4x 16.

17. Direct; 18. Indirect; xy = 15 19. 22, 27

20. -47, -60 21. 4 22. -7 23. 3 24. -11

y 5 214x

y 532x

O

4

�4

�4

4x

yx y

-6 2

0 0

6 -2

O

4

8

4 8x

yx y

4 5

6 3

8 1

f(x) 5x3

e 29, 2 fe22, 21

3, 0, 13 f

x

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om G

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Time

y 552x

y 5 223xy 5 22xy 5

13x

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-2 5

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yx y

-2 -1

0 2

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uphill

downhill

Speed of Train

Algebra 1 Chapter 5 Answers 43

Chapter 5 Answers (continued)

Alternative Assessment, Form CTASK 1 Scoring Guide:

a.

b. positive

c. The size increases with height.

3 Scatter plot is accurately drawn with no errors.Explanation of correlation is thorough and clearlydemonstrates an understanding of the underlyingmathematical principals.

2 Scatter plot is correctly drawn, with only minor errors in scale and accuracy. Explanation of correlation is well stated.

1 Scale and accuracy of scatter plot are partially correct.Correlation may be incorrect.

0 Student makes no attempt, or no solution is presented.

TASK 2 Scoring Guide:

3 Student writes a story and makes a sketch that showssignificant understanding of the relationship betweentime and distance. Variables relate to the story and areused correctly.

2 The sketch is mostly correct but contains minor errorsrelated to the story or the variables.

1 The response is partially satisfactory, but there are major errors.

0 Student makes no attempt, or no solution is presented.

TASK 3 Scoring Guide:

a.–c. Check students’ work.

d. 16; the dependent variable is y and the independentvariable is x.

3 Student writes explanations that show an in-depthunderstanding of the relevant mathematical ideas andprocesses. Examples presented are appropriate andclearly support the student’s definition. Function rule iscorrect based on table of values.

2 Definition and explanations are essentially correct butcould be more thorough. Graphs are mostly correct.Function rule relates to table of values.

1 Definition and explanations are incorrect. Examples orfunction rule are incorrect.

0 Student makes no attempt, or no solution is present.

TASK 4 Scoring Guide:

a. Answers may vary. Sample: The constant of variation for a linear equation equals the slope of the line thatrepresents the equation.

b. Table 1: y varies inversely with x, ;

Table 2: y varies directly with x,

3 All parts of the task are complete. Explanations arecomplete, and tables are correct. All calculations are correct.

2 All parts of the task are complete. Explanations are cor-rect but not complete. Tables and calculations containminor errors.

1 Some parts of the task are missing. Explanations areincomplete or incorrect. Computations are incorrect.

0 Student makes no attempt, or no solution is present.

Cumulative Review1. D 2. G 3. B 4. H 5. A 6. J 7. C 8. F 9. C

10a. 10b. 11a. -21 11b. 4 12. Answers may vary.Sample: a is number of hours you would need to work annuallyto average 15 h of work per month. 13. 21 ft 14. 157%

12

23

y 5 234x

y 5 28x

Boy's Clothing Sizes

Size

Hei

ght (

in.)

2

102030405060

4 6 8 10 12 14

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Chapter 5 Answers (continued)

Answers Algebra 1 Chapter 544

15. Answers may vary. Sample:

16. Answers may vary. Sample:

17. The graph is a function if a vertical line passes through thegraph only once. 18. {5, 7, 8} 19. Answers may vary. Sample:

20. 21. -2 22. 2526

absolutevalue

quadratic

O

y

x

Time0

Spee

d

uphill

downhill

Cost of T-Shirt0

Num

ber

of T

-Shi

rts

Sold

10

20

40

60

80

20 30 40

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