Chapter 5 Answers
9.
Practice 5-1
Speed
10.
Speed vs. Time
Speed
3. The distance from home is not changing.
4. The distance from home decreases.
5. The distance from home increases.
6.
Mountain Hike
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, the
speed is decreasing. In sections 1 to 2, 4 to 5, and 7 to 8, the
speed is constant. At 0, 3, 6, and 9, the car is not moving.
Elevation
All rights reserved.
0 1 2 3 4 5 6 7 8 9
Time
Time
0
0
0
1
2
Time
3
11.
7.
Time
Speed vs. Time
Speed
Answers may vary. Sample: In section 0 to 1, the hiker is
ascending. In section 1 to 2, the hiker’s elevation is constant. In
section 2 to 3, the hiker is descending.
Trip to School
0
0
1
2
Time
3
Answers may vary. Sample: In section 0 to 1, speed is increasing. In section 1 to 2, speed is constant. In section 2 to 3, speed
is decreasing.
8.
0
Plane Trip
Time
Speed vs. Time
Speed
Speed
12.
Height
Above Ground
© Pearson Education, Inc., publishing as Pearson Prentice Hall.
Trip to Store
Speed
1. The student is traveling at a constant speed.
2.
Trip to School
0
Time
Practice 5-2
1. 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. e 0, 12 f 23a. d(t) = 60t 23b. {60, 300, 600}
Time
23c. Domain is time and range is distance traveled.
Answers may vary. Sample: Where the graph is increasing, the
height above the ground is increasing. Where the graph is flat,
the height is not changing. Where the graph is decreasing, the
height above the ground is decreasing.
Answers
Algebra 1 Chapter 5
35
(continued)
For Exercises 1–11, answers may vary. Sample:
1.
2.
x
f(x)
-1
0
0
1
1
2
2
3
x
f(x)
-2
-4
-1
-2
0
0
1
2
3
2
f(x)
x
O
1 2
7.
2
1
O x
1
21
4.
5.
36
x
f(x)
-1
-5
0
-2
1
1
2
4
x
f(x)
0
-2
2
1
4
4
6
7
x
f(x)
-2
-1
0
0
2
1
4
2
f(x)
-3
3
0
1
3
-1
6
-3
4
3
2
1
21
1
x
1 2
2
9.
f(x)
8
6
4
2O
x
2 4 6
2
1
f(x)
x
O
1
2
3
4
1
Algebra 1 Chapter 5
10a.
4
x
f(x)
-2
5
-1
2
0
1
1
2
2
5
x
f(x)
-2
-2
0
2
2
-2
3
-7
8
7
6
5
4
3
2
f(x)
x
O
1 2 3
f(x)
1
32
1
2
3
4
x
f(x)
-3
-6
4
2
0
-3
42
2
3
0
6
3
g
x
6
O
42
2
321
f(x)
O
f(x)
4
3
4 f(x)
8.
3.
x
All rights reserved.
6.
Practice 5-3
x
O
1 2 3
f(x)
x
O
4 6
6
d(g)
0
0
1
22
2
44
30
20
10
321
g
O
1 2 3
30 D(g)
10b. 231 mi 10c. Yes; g is continuous but it only makes
sense for positive values.
Answers
© Pearson Education, Inc., publishing as Pearson Prentice Hall.
Chapter 5 Answers
Chapter 5 Answers
11a.
n
T(n)
1
3.50
2
4.00
3
4.50
4
5.00
5
4
3
2
1
(continued)
18.
T(n)
4
2
2
2
n
O
1 2 3 4
All rights reserved.
13.
6
5
4
3
2
14.
© Pearson Education, Inc., publishing as Pearson Prentice Hall.
2
21
1
2
15.
f(x)
O
2
2 4 6
2
4
6
2
x
y
6
4
2
O
2
2
2
4
2
4
6
8
2
23.
x
O
2 4
y
2
x
2 O
2
2 a2 1 , 2 17 b
4
x
8
For Exercises 24 – 26, answers may vary. Sample:
24.
2
Answers
22.
x
f(x)
O
2
2 2 4 6
x
O
1 2 3 4 5 6 7
2
2
2
2
2
y
y
O
O
f(x)
21.
x
O
42
2 4
2
4
6
8
17.
6
5
4
3
2
1
x
2 O
6
4
2
12
10
8
6
4
2
20.
2
x
O
2 4 6 8
2
f(x)
16.
x
y
x
O
1 2
f(x)
21
y
2
11b. $6.00 11c. No; n is a discrete variable.
12.
19.
f(x)
8
12 x
26.
25.
x
y
x
y
0
-1
0
2
1
1
1
-1
2
3
2
-4
x
y
-2
2
-1
0
0
0
1
2
Algebra 1 Chapter 5
37
Chapter 5 Answers
(continued)
3.
Practice 5-4
1. 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 + 10n
5b. $110 6. ƒ(x) = 12 x 7. ƒ(x) = x2 8. ƒ(x) = 20 - x
9a. N(b) = 12b 9b. 192 pens 10a. C(n) = 20 - 1.25n
10b. $13.75 10c. no 11a. P(n) = 9.50a - 209
11b. $19.00 11c. 22 shirts
Photo Trip
Total Distance
downhill
Practice 5-5
downhill
uphill
taking
photos
1. yes; 5 2. yes; -4 3. no 4. no 5. yes; 3 6. yes; 3
Time
4. The flat part of the graph. When you are taking pictures,
you are not moving. 5. The ride down Lookout Knoll. When
you ride down, you go faster and cover the distance in a
shorter amount of time.
6.
Photo Trip
Practice 5-6
Distance from Base
1
1. xy = 54 2. xy = 18 3. xy = 6 4. xy = 91 5. xy = 72
6. xy = 3.92 7. xy = 484 8. xy = 76 9. xy = 10 10. 10
11. 8 12. 16 13. 2 14. 37 13 15. 625 16. 4 17. 6 18. 2
25
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 = 11x
30. Direct variation; y = 4.5x 31. Inverse variation; xy = 36
32. Direct variation; y = 2.1x 33. Direct variation; y = 6.4x
34. Inverse variation; xy = 6 35. Inverse variation; xy = 18
36a. 5 m3 36b. 2 atm 36c. 19.2 m3 37a. 1.5 h 37b. 192 ft/s
Practice 5-7
1. 6 2. -3 3. -5 4. 3 5. 21 6. 212 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. 272 , 292 17. 7.9, 9.2 18. -26.6, -35.7
19. 231 , 22 20. -4 1 , -6 1 21. 44, 94, 994
2
4
22. -18, -58, -778 23. 31, 66, 696 24. -31, -46, -316
, 2 197 26. 2.7, 7.7, 97.7 27. 404, 909, 9999
25. 2 74 , 2 17
4
4
28. -397, -892, -9802 29. 0.6, -4.9, -103.9
30. 24 1 , 25 3 , 228 1 31. yes; common diff. = -0.2
2
4
4
32. no 33. no 34. no 35a. $100, $135, $170, $205
35b. $35 35c. $240, $905, $1745, $2585
downhill
uphill
taking
photos
0
Time
Reteaching 5-2
1. 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 5-3
1.
2.
y
y
2
2
x
2
O
2
2
x
2
O
2
2
Reteaching 5-1
1. It shows total distance traveled. 2. It shows elapsed time.
38
Algebra 1 Chapter 5
All rights reserved.
0
Answers
© Pearson Education, Inc., publishing as Pearson Prentice Hall.
5
3
7. yes; 2 8. no 9. no 10. yes; 2 11. no 12. yes; 29
5
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 = 2x
26. yes; y 5 23 x 27. no 28. yes; y = 1.4x 29a. V 5 65 T
29b. 350 mL 30a. g = 4c 30b. 96 31. $75
Chapter 5 Answers
3.
4.
y
2
x
5.
6.
x
x
at a constant speed, decelerating, and then continuing at a constant speed 3. amount of an element undergoing decay
4. height of a growing child over the year 5. amount of money
in an investment account compounded 6. height of a person
when riding a ferris wheel 7. the closing prices of the stock
market 8. the rate of postage to mail letters by the ounce
2
2
2
Enrichment 5-2
O
1. 0.3, 0.65, 0.1, 0.5; {(30, 0.3), (65, 0.65), (10, 0.1), (50, 0.5)}
2. yes;
y
2
x
0.6
2
0.4
7.
0.2
8.
y
y
2
2
x
x
2
O
2
2
O
2
2
2
x
O
20 40 60
x 4. 0.15; 0.6; 1.8 5. 0.025; 0.4; 3.6
3. f(x) 5 100
6. 0.45; 0.3; 0.1 7. 5.5; 10; 22
8. yes;
y
60
Percent
All rights reserved.
2
2
y
2
O
O
2
O
y
2
1–8. Answers will vary. Samples:
1. the temperature during the day 2. a car accelerating, going
2
2
2
Enrichment 5-1
y
4
4
(continued)
Reteaching 5-4
© Pearson Education, Inc., publishing as Pearson Prentice Hall.
1. ƒ(x) = 3x 2. ƒ(x) = x - 1 3. ƒ(x) = x2
40
20
4. /(w) = 4w + 2 5. w(/) = 1 / 6. c(a) = 0.99a
2
7. d(t) = 65t 8. v(q) = 0.25q 9. e(n) = 8.25n 10. f(d) = 3d
Reteaching 5-5
1. yes; -3 2. no 3. yes; -2 4. yes; 1 5. yes; 2 6. no
Reteaching 5-6
1. 151; 132 2. $10.22
3.
Price
No. Sold
$12.50
132
$12.00
138
$11.50
144
$11.00
151
$10.22
162
x
O
2
4
Hour
6
9. no, 6% is paired to two different values. 10. yes; each first
element is paired only once.
Enrichment 5-3
1.
2.
y
y
2
2
x
2
O
2
2
x
2
O
2
2
Reteaching 5-7
1. 7 2. -4 3. 11 4. -6, -8 5. 8, 11
6. -37, -42 7. A(n) = 2 + 7(n - 1); 30; 65
8. A(n) = 5 - 4(n - 1); -11; -31
9. A(n) = -52 + 11(n - 1); -8; 47
Answers
Algebra 1 Chapter 5
39
Chapter 5 Answers
3.
(continued)
4.
y
15.
y
2
O
x
2
2
O
2
y
2
2
x
O
x
2
2
O
2
2
2
7.
8.
y
Enrichment 5-4
1. V 5 /hd
2. 72 3. 3.5 4. 4 5. 4, 4, 4 6. 225 7. 4.6
2
8. 3.8 9. p = i - e - t 10. $8000 11. $52,000 12. $3889
y
2
2
Enrichment 5-5
x
O
2
2
O
2
5. 10; 5 c; 2 21 tsp; 10 tbs; 2 12 tsp 6. yes 7. no 8. yes
2
9.
9. yes; 10. 32 oz; 1 c; 1 c; 4 tsp; 12 tsp; 8 c; 32 oz
10.
y
Enrichment 5-6
y
2
1. Answers may vary. Sample: (2, 10), (4, 5), (5, 4)
2
x
O
x
2
2
2
O
12.
y
y , domain
2 10
2
4 5
4
5 4
5
2
2
x
x
O
2
2
2
2
2
13.
O
14.
y
x
2
2
O
2
2
x f(x) , x g(x) ,
2 6
2 -6
3 -4
3 4
4 -3
4 3
12
f(x) 5 x for x .
h(x) 5 12
x for x ,
x i(x) ;
-2 6
-3 4
-4 3
0, g(x) 5 2 12
x for x . 0,
0, i(x) 5 2 12
x for x , 0
x
-2
-3
-4
h(x) ,
-6
-4
-3
Leonardo Fibonacci
2
x
O
4
5
10
Enrichment 5-7
y
2
range
3. Yes; For every point, xy = -12 and xy = 12.
4. Answers may vary. Sample:
y
2
2
2. Answers may vary. Sample: x
2
11.
2
1. 1 21 c 2. 30 c 3. 8 pies 4. 4 tbs (4 full pies)
x
2
17. decreases without bound, increases without bound
18. increases without bound, decreases without bound
19. approaches 0, increases without bound
20. increases without bound, approaches 0
21. decreases without bound, increases without bound
22. approaches 0, increases without bound
2
Chapter Project
Activity 1: Doing
Check students’ work.
Activity 2: Graphing
Check students’ work.
40
Algebra 1 Chapter 5
All rights reserved.
6.
y
2
x
O
2
5.
2
x
O
Answers
© Pearson Education, Inc., publishing as Pearson Prentice Hall.
2
2
y
2
x
2
16.
y
Chapter 5 Answers
(continued)
Activity 3: Writing
21.5 s, the time it takes 5 people in a row to say the tongue
twister; It takes 0 people in a row 0 s to say the tongue twister;
Solve 4.3n = 34.4 for n; Check students’ work.
2.
Activity 4: Analyzing
Check students’ work.
✔ Checkpoint Quiz 1
x
y
-1
21
2
0
1
2
1
23
2
25
4
-1
23
4
21
2
1.
All rights reserved.
Height
3.
x
-2
5
-1
3
Years
0
1
1
-1
2
-3
2.
Distance
4.
x
g(x)
-2
6
-1
3
0
0
1
-3
2
-6
Time
3.
y
2
2
O
2
x
2
;
y
2
x
2
O
2
2
;
; -3
y
2
x
2
O
2
2
5. A(t) = 7.75t 6. C(n) = 0.49n 7. 6 8. -14.6
Population
9. 12 10. A(t) = 5.65t
Chapter Test, Form A
1. Answers may vary. Sample:
Height of Elevator
Stopped
Time (hours)
4. No, the graph fails the Vertical Line Test.
Down
5. -2 6. 2 5 7. 1 8. 5 9. -1 10. 12
2
2
Height
© Pearson Education, Inc., publishing as Pearson Prentice Hall.
f(x)
;
✔ Checkpoint Quiz 2
1.
;
x
y
-2
-10
-1
-5
0
0
1
5
2
10
Answers
;5
y
0
Down
Going up
Time
4
x
4
O
4
4
Algebra 1 Chapter 5
41
Chapter 5 Answers
(continued)
2. Answers may vary. Sample:
1.
Speed
uphill
Distance from Ground
Chapter Test, Form B
Speed of Train
y
x
Time
downhill
2. Domain {1, 2, 3, 5}
Range {5, 9, 11, 12}
3. yes 4. no 5. If any x-coordinate occurs more than once
with 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:
x
y
-2
-1
0
2
2
5
y
2
x
2
O
2
2
9. Answers may vary. Sample:
x
y
-2
5
-1
-1
0
-3
1
-1
2
5
3
15
Range e 2 , 2 f
9
4. f(x) 5 x
5. ƒ(x) = x + 2 6. -38 7. 19
3
8. {10, 31, 38.5} 9. {-5, 4, 7, 16}
10. Tables may vary. Sample:
x
y
4
5
6
3
8
1
y
8
4
x
y
O
4
8
2
x
2
O
2
2
10. ƒ(x) = 35x 11. ƒ(x) = 5.50x 12. ƒ(x) = 5.00 - 0.89x
13. ƒ(x) = 2x + 1 14. f(x) 5 212 x 15. Answers will
vary. Sample: The amount of change you would get from
spending a $10 bill. 16a. ƒ(x) = $13.50x 16b. $81.00
16c. 14h 17. y 5 13 x 18. y 5 22x 19. y 5 2 23 x
20. y 5 25 x 21. yes; y = -4x 22. no 23. 36 24. 16
25. -45.6 26. A relation is a function when each x-value is
paired 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
42
3. Domain e 22, 2 13 , 0, 13 f
All rights reserved.
Time
Algebra 1 Chapter 5
11. Tables may vary. Sample:
x
y
-6
2
0
0
6
-2
y
4
x
4
O
4
4
12. ƒ(x) = 1.29x 13. ƒ(x) = 12x 14a. ƒ(x) = 1.65x
14b. $234.30 15. y = 4x 16. y 5 3 x
2
1
17. Direct; y 5 2 4 x 18. Indirect; xy = 15 19. 22, 27
20. -47, -60 21. 4 22. -7 23. 3 24. -11
Answers
© Pearson Education, Inc., publishing as Pearson Prentice Hall.
0
Chapter 5 Answers
(continued)
Alternative Assessment, Form C
3 Student writes explanations that show an in-depth
understanding of the relevant mathematical ideas and
processes. Examples presented are appropriate and
clearly support the student’s definition. Function rule is
correct based on table of values.
TASK 1 Scoring Guide:
a.
Height (in.)
Boy's Clothing Sizes
60
50
40
30
20
10
2 Definition and explanations are essentially correct but
could be more thorough. Graphs are mostly correct.
Function rule relates to table of values.
1 Definition and explanations are incorrect. Examples or
function rule are incorrect.
All rights reserved.
2 4 6 8 10 12 14
Size
TASK 4 Scoring Guide:
b. positive
a. Answers may vary. Sample: The constant of variation
c. The size increases with height.
for a linear equation equals the slope of the line that
represents the equation.
8;
b. Table 1: y varies inversely with x, y 5 2x
3 Scatter plot is accurately drawn with no errors.
Explanation of correlation is thorough and clearly
demonstrates an understanding of the underlying
mathematical 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:
© Pearson Education, Inc., publishing as Pearson Prentice Hall.
0 Student makes no attempt, or no solution is present.
3 Student writes a story and makes a sketch that shows
significant understanding of the relationship between
time and distance. Variables relate to the story and are
used correctly.
2 The sketch is mostly correct but contains minor errors
related to the story or the variables.
1 The response is partially satisfactory, but there are
major errors.
3
Table 2: y varies directly with x, y 5 2 3 x
4
All parts of the task are complete. Explanations are
complete, and tables are correct. All calculations are
correct.
2 All parts of the task are complete. Explanations are correct but not complete. Tables and calculations contain
minor errors.
1 Some parts of the task are missing. Explanations are
incomplete or incorrect. Computations are incorrect.
0 Student makes no attempt, or no solution is present.
Cumulative Review
1. D 2. G 3. B 4. H 5. A 6. J 7. C 8. F 9. C
10a. 23 10b. 12 11a. -21 11b. 4 12. Answers may vary.
Sample: a is number of hours you would need to work annually
to average 15 h of work per month. 13. 21 ft 14. 157%
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 independent
variable is x.
Algebra 1 Chapter 5
Answers
43
Chapter 5 Answers
17. The graph is a function if a vertical line passes through the
graph only once. 18. {5, 7, 8} 19. Answers may vary. Sample:
y
80
absolute
value
O
60
40
x
20
0
10
20
30
40
Cost of T-Shirt
Speed
16. Answers may vary. Sample:
quadratic
All rights reserved.
Number of T-Shirts Sold
15. Answers may vary. Sample:
(continued)
5 21. -2 22. 2
20. 26
downhill
uphill
Time
© Pearson Education, Inc., publishing as Pearson Prentice Hall.
0
44
Answers
Algebra 1 Chapter 5