1. technology and computing
2. computer certification

Answers to All Exercises
CHAPTER 4 • CHAPTER
4
CHAPTER 4 • CHAPTER
REFRESHING YOUR SKILLS FOR CHAPTER 4
Add 7 to each side.
Multiply each side by _13 or divide each side by 3.
Add 2 to each side or subtract 2 from each side.
Square each side.
Add 6 to each side or subtract 6 from each side.
Answers to All Exercises
1a.
1b.
1c.
1d.
1e.
2a. x 33
2b. x 1 or x 15
2c. x 5 or x 3
2d. y 57
2e. no solution
3. The possible student answers for 2e, x 2 and
x 2, do not check, so they are not valid solutions.
The absolute value of a number cannot be negative.
34
ANSWERS TO ALL EXERCISES
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1a. A
2a.
1b. C
2b.
1c. D
1d. B
2c.
6c. Time in minutes is the independent variable;
the drink’s temperature in degrees Fahrenheit is the
dependent variable.
Temperature (°F)
LESSON 4.1
Time (min)
Speed (ft/s)
6e. Time in minutes is the independent variable;
your height above the ground in feet is the dependent variable.
Height (ft)
Time (min)
Amount ($)
7a. Time in years is the independent variable; the
amount of money in dollars is the dependent variable. The graph will be a series of discontinuous
segments.
Time (yr)
7b. Time in years is the independent variable; the
amount of money in dollars is the dependent variable. The graph will be a continuous horizontal
segment, because the amount never changes.
Time (yr)
Braking
distance (ft)
6b. The car’s speed in miles per hour is the
independent variable; the braking distance in feet is
the dependent variable.
Time (s)
Amount ($)
Height (ft)
Time (s)
6d. Time in seconds is the independent variable;
the acorn’s speed in feet per second is the dependent
variable.
Answers to All Exercises
3a. decreasing at a steady rate, suddenly becoming
constant, then suddenly increasing at the same rate it
was decreasing at
3b. first decreasing, then increasing back to the same
level, without any sudden changes in rate
3c. rapidly increasing from 0; suddenly changing
to rapidly decreasing, until half the value is reached;
constant, then suddenly rapidly decreasing at a
constant rate until reaching 0
4a. Possible answer: The curve might describe the
relationship between the amount of time the ball is in
the air and how far away from the ground it is.
4b. possible answer: seconds and yards
4c. possible answer: domain: 0 t 10 s; range: 0 h 70 yd
4d. No, the horizontal distance traveled is not measured.
5. Sample answer: Zeke, the fish, swam slowly, then
more rapidly to the bottom of his bowl and stayed
there for a while. When Zeke’s owner sprinkled fish
food into the water, Zeke swam toward the surface to
eat. The y-intercept is the fish’s depth at the start of
the story. The x-intercept represents the time the fish
reached the surface of the bowl.
6a. Time in seconds is the independent variable; the
height of the ball in feet is the dependent variable.
Speed (mi/h)
ANSWERS TO ALL EXERCISES
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Foot length (in.)
Price per gallon
7d. Answers will vary but should be in the form of
a discrete graph.
Day of the month
Maximum temperature (°F)
Answers to All Exercises
7e. The day of the month is the independent variable; the maximum temperature in degrees Fahrenheit is the dependent variable. The graph will be
discrete points, because there is just one temperature reading per day.
Day of the month
Cost ($)
8. sample answer: the cost of parking your car at a lot
that charges a certain fixed price for up to an hour and
then half as much for each additional hour or fraction
thereof
9b. Car A will be in the lead because it is always going
faster than Car B, which means it has covered more
distance.
10a. Let l represent the length of the rope in meters,
and let k represent the number of knots; l 1.70 0.12k.
10b. Let b represent the bill in dollars, and let c
represent the number of CDs purchased; b 7.00 9.50(c 8) where c 8.
11a. Let x represent the number of pictures, and
let y represent the amount of money (either cost or
income) in dollars; y 155 15x.
11b. y 27x
Amount of money ($)
Shoe size
7c. Foot length in inches is the independent variable; shoe size is the dependent variable. The
graph will be a series of discontinuous horizontal
segments, because shoe sizes are discrete.
y
400
320
240
160
80
Cost: y 155 15x
Income: y 27x
x
2 4 6 8 10 12 14 16
Number of pictures
11c. 13 pictures
11d. The income, $216, is less than the cost, $275.
12a. $142,784.22
12b. $44,700.04
12c. $0 (You actually pay off the loan after 19 yr 10 mo.)
12d. By making an extra $300 payment per month
for 20 yr, or $72,000, you save hundreds of thousands
of dollars in the long run.
13a. 3x 5y 9
13b. 6x 3y 21
13c. x 2, y 3
13d. x 2, y 3, z 1
Time (h)
9a. Car A speeds up quickly at first and then less
quickly until it reaches 60 mi/h. Car B speeds up
slowly at first and then quickly until it reaches 60 mi/h.
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ANSWERS TO ALL EXERCISES
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7a, c, d.
LESSON 4.2
y
1a. Function; each x-value has only one y-value.
1b. Not a function; there are x-values that are paired
with two y-values.
1c. Function; each x-value has only one y-value.
2a. 17
2b. 27
2d. 11
2e. 11
3
___
2c. 19
5b. The time the money has been in the bank is the
independent variable; function.
5c. The amount of time since your last haircut is the
independent variable; function.
5d. The distance you have driven since your last fillup is the independent variable; function.
6a. Let x represent the price of the calculator in
dollars, and let y represent the sales tax in dollars.
y
–25
(7, 20.8)
25
x
–25
7b. 20.8
7d. 4
8. domain: 6 x 5; range: 2 y 4
9a. possible answer:
y
x
9b. possible answer:
9c.
Answers to All Exercises
3. B
4a. 18 R
4b. 5 E
4c. 14 N
4d. 5 E
4e. 4 D
4f. 5 E
4g. 19 S
4h. 3 C
4i. 1 A
4j. 18 R
4k. 20 T
4l. 5 E
4m. 19 S
5a. The price of the calculator is the independent
variable; function.
(–4, 27.4)
y
y
x
x
10a. 104
10b. f (n) 3(n 1)2 4
10c. f (x 2) 3(x 3)2 4
10d.
x
6b. Let x represent the time in months, and let y
represent the account balance in dollars.
y
x
6c. Let x represent the time in days, and let y
represent the length of your hair.
y
x
6d. Let x represent the distance you have driven in
miles, and let y represent the amount of gasoline in
your tank in gallons.
y
The graphs are the same shape. The graph of f (x 2)
is shifted 2 units to the left of the graph of f (x).
11. Let x represent the time since Kendall started
moving, and let y represent his distance from the
motion sensor. The graph is a function; Kendall can
be at only one position at each moment in time, so
there is only one y-value for each x-value.
12a. 155.68 in.
12b. approximately 16.5 s
13a. 54 diagonals
13b. 20 sides
x
ANSWERS TO ALL EXERCISES
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18a.
Height
14a.
18b.
x
3
x
1
x
x2
3x
x x2
x
7
7x
21
2 2x
2
Time
Height
14b.
18c.
Time
2x
14c.
Height
x 2x 2 10x
10 20x 100
Answers to All Exercises
15. Sample answer: Eight students fall into each
quartile. Assuming that the mean of each quartile
is the midpoint of the quartile, the total will be
8(3.075 4.500 5.875 9.150), or $180.80.
16. (7, 25.5)
17a. possible answer:
f(x)
19a.
Distance (m)
Time
y
5
C(t) 0.2 0.5x
4
(4, 2.2)
3
2
1
A(t) 4.2 0.5x
0
x
17b. possible answer:
f (x)
–10
10
1 2 3 4 5 6
Time (s)
x
19b. A(t) 0.2 0.5t; C(t) 4.2 0.5t
19c. (4, 2.2); After 4 s, Bao is 2.2 m from both Alice
and Carlos.
3
10
–3
x
17c. possible answer:
f (x)
10
–2
38
x
ANSWERS TO ALL EXERCISES
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LESSON 4.3
__
__
__
12a. 80.8
__
12b. y 1 x 65
5
12c. 95 points
13a. x 15
13b. x 31
13c. x 21
13d. x 17.6
14. yˆ 29 3 x
2
2
___ __
ANSWERS TO ALL EXERCISES
DAA2TE_985_ANS_a.indd 39
Answers to All Exercises
1. y 3 2 (x 5)
3
2. translated right 3 units
3a. 2(x 3), or 2x 6
3b. 3 (2)(x 2), or 2x 1
3c. 5 (2)(x 1), or 2x 3
__
48(x 1.4) or
4a. y 4.4 1.1__
y 3.18 1.148(x 5.2)
___
4b.__y 2.4 1.148 (x 1.4) or y 5.18 1.148(x 5.2)
5a. y 3 4.7x
5b. y 2.8(x 2)
5c. y 4 (x 1.5), or y 2.5 x
6a. y 2 f (x)
6b. y 2 f (x 1)
6c. y 5 f (x 2)
6d. y 2 f (x 1)
7. y 47 6.3(x 3)
8a. Brian stood about 1.5 m behind Pete, and he
started his motion sensor 2 s later than Pete started his.
8b. y 1.5 f(x 2)
_
9a. (1400, 733.3)
_
9b. (x + 400, y + 233.3)
9c. 20 steps
10a. i. a 4, b 3, c 12
10a. ii. a 1, b 1, c 5
10a. iii. a 7, b 1, c 1
10a. iv. a 2, b 4, c 2
10a. v. a 0, b 2, c 10
10a. vi. a 3, b 0, c 6
__ __
10b. y c a x; y-intercept: c ; slope: a
b b
b
b
4
_
10c. i. y-intercept: 4; slope: 3
10c. ii. y-intercept: 5; slope: 1
10c. iii. y-intercept: 1; slope: 7
10c. iv. y-intercept: _12 ; slope: _12
10c. v. y-intercept: 5; slope: 0
10c. vi. y-intercept: none; slope: undefined
10d. i. 4x 3y 20
10d. ii. 4x 3y 8
10d. iii. 4x 3y 24
10d. iv. 4x 3y 9
10d. v. 4x 3y 7
10d. vi. 4x 3y 10
10e. ax by c ah bk
11a. 12,500. The original value of the equipment is
$12,500.
11b. 10. After 10 yr, the equipment has no value.
11c. 1250. Every year, the value of the equipment
decreases by $1,250.
11d. y 12,500 1,250x
11e. after 4.8 yr
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3/26/09 7:15:41 PM
LESSON 4.4
1a.
1b.
1c.
1d.
2a.
y x2 2
y x2 6
y (x 4)2
y (x 8)2
y x2 5
y
5
–5
5
x
6d. y (x 6)2 2
7a. y (x 5)2 3
7b. (5, 3)
7c. (6, 2), (4, 2), (7, 1), (3, 1). If (x, y) are the
coordinates of any point on the black parabola, then
the coordinates of the corresponding point on the red
parabola are (x 5, y 3).
7d. Segment b has length 1 unit, and segment c has
length 4 units.
8a.
y
5
–5
5
2b. y x2 3
y
x
–5
5
8b.
Answers to All Exercises
–5
5
y
x
5
–5
5
–5
2c. y (x 3)2
x
–5
y
9a.
5
Number of
–5
5
x
teams (x )
Number of
–5
games ( y )
2d. y (x 4)2
y
4
5
6
7
8
9
10
12
20
30
42
56
72
90
9b. The points appear to be part of a parabola.
5
–5
5
x
–5
3a.
3b.
3c.
3d.
4a.
4b.
4c.
4d.
5a.
5b.
5c.
6a.
6b.
6c.
40
translated vertically 3 units
translated vertically 4 units
translated horizontally 2 units
translated horizontally 4 units
translated horizontally 3 units
translated horizontally 3 units
translated vertically 2 units
translated vertically 2 units
x 2 or x 2
x 4 or x 4
x 7 or x 3
y (x 2)2
y (x 2)2 5
y (x 6)2
9c. y (x 0.5)2 0.25
9d. 870 games
10a. x 9 or x 1
10b. x 4 or x 10
___
10c. 1 27
__
10d. x 6 8
11a. The graph will be translated horizontally
5 points (one bin).
11b. The graph will be translated horizontally
10 points (two bins).
12a. B
12b. C
ANSWERS TO ALL EXERCISES
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C
51
A
E
C
D
B
X
Time
Luxury
Mertz
32
24
14.
Distance
13a. Let m represent the miles driven, and let C
represent the cost of the one-day rental. Mertz: C 32 0.1m; Saver: C 24 0.18m; Luxury: C 51.
13b.
Saver
m
100
150
190
13c. If you plan to drive less than 100 mi, then rent
Saver. At exactly 100 mi, Mertz and Saver are the
same. If you plan to drive between 100 mi and 190 mi,
then rent Mertz. At exactly 190 mi, Mertz and Luxury
are the same. If you plan to drive more than 190 mi,
then rent Luxury.
15a. Possible answer: the walker stayed 3.8 m from
the sensor for 1.2 s and then walked at a constant
0.84 m/s toward the sensor.
15b. When is the walker 2 m from the observer?
15c. After about 3.34 s, the walker is 2 m from the
observer.
16a. The slopes vary, but the y-intercept is always 4.
16b. The graphs move up or down, but they all have
slope 2.
Answers to All Exercises
ANSWERS TO ALL EXERCISES
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__
__
_____
y x 3
1b. y x 5
_____
_____
y x 5 2
1d. y x 3 1
_____
y x 1 4
translated horizontally 3 units
translated horizontally 3 units
translated vertically 2 units
translated vertically 2 units
iii
i
ii
4b.
y
y
5
5
y f (x)
x
5
Answers to All Exercises
–5
–5
5
y x ; y2 x
Neither parabola passes the vertical line test.
_____
i. y x 4
__
ii. y x 2
i. y 2 x 4
ii. (y 2)2 x
possible answer:
y
x
y f (x)
–5
–5
__
7b.
8a.
8b.
8b.
8c.
8c.
9a.
4c.
Distance (mi)
1a.
1c.
1e.
2a.
2b.
2c.
2d.
3a.
3b.
3c.
4a.
__
7a. y x and y x
LESSON 4.5
250
200
150
100
50
Arthur
Jake
x
y
0
5
x
5
y f (x)
–5
–5
__
5a. y x
__
5b. y x 3
_____
5c. y x 6 5
___
5d. y x
________
5e. y (x 2) 3,
_______
or y x 2 3
6a. possible answers: (4, 2), (3, 1), and (0, 0)
_____
6b. y x 4 2
2 4 6 8
Time (h)
9b. y f (x 1) 250
9c. y g (x 1) 250
10a. y x 2
10b. y x 2 2
10c. y (x 6)2
10d. y (x 6)2 3
11. y 2 [(x 5) 3]2 4, or y (x 2)2 2
12a. 2
12b. 2
12c. 1, 3
12d. 3
12e. 3
12f. 3
12g. 1
_____
13a. S 5.50.7D
13b.
S
D
13c. approximately 36 mi/h
S
1 ___
13d. D ___
0.7 5.5 ; the minimum braking distance,
when the speed is known
13e.
2
_____
6c. y x 2 3
42
ANSWERS TO ALL EXERCISES
DAA2TE_985_ANS_a.indd 42
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It is a parabola, but the negative half is not used
because the distance cannot be negative.
13f. approximately 199.5 ft
14a. Not a function; many states have more than one
area code.
14b. function
14c. Not a function; there are many common
denominators for any pair of fractions.
14d. Possible answer: Function; the sun rises at only
one time on each day of a given year.
15a. x 293
15b. no solution
15c. x 7 or x 3
15d. x 13
2
16. y (x 6) 4
17a. y 1x 5
2
__
__
17b. y 1 (x 8) 5
2
y
(2, 6)
(–8, 1)
(10, 6)
(0, 1)
x
__
__
17c. y 1 x 5 4, or y 4 1 x 5
2
2
17d. Both equations are equivalent to y 1x 1.
2
18a. 35, 37.5, 41.5, 49, 73
18b.
__
35 40 45 50 55 60 65 70 75
18c. 11.5
18d. 70 and 73
19. (8, 7)
Answers to All Exercises
ANSWERS TO ALL EXERCISES
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LESSON 4.6
1a. y 兩x兩 2
1b. y 兩x兩 5
1c. y 兩x 4兩
1d. y 兩x 3兩
1e. y 兩x兩 1
1f. y 兩x 4兩 1
1g. y 兩x 5兩 3
y
1h. __ 兩x 6兩, or y 3兩x 6兩
3
x
1i. y | __
4|
1j. y (x 5)2
1 兩x 4兩
1k. 2y 兩x 4兩, or y __
2
1l. y 兩x 4兩 3
1m. y (x 3)2 5
_____
1n. y x 4 3
y
x 3 , or y 2 _____
x3
1p. ___ _____
2
3
3
2a. horizontal dilation by a factor of 3
2b. reflection across the y-axis
2c. horizontal dilation by a factor of _13
2d. vertical dilation by a factor of 2
2e. reflection across the x-axis
2f. vertical dilation by a factor of _12
3a. y 2(x 5)2 3
3b. y 2 x 1 5
3
_____
3c. y 2 x 6 7
3
4. For b 0, the graphs of y b兩x兩 and y 兩bx兩
are equivalent. For b 0, the graph of y b兩x兩 is a
reflection of y 兩bx兩 across the x-axis.
5a. 1 and 7; x 1 and x 7
5b. x 8 and x 2
Answers to All Exercises
|
|
|
|
8. The parabola is dilated vertically by a factor of 3,
dilated horizontally by a factor of 4, and translated
horizontally 7 units and vertically 2 units.
y
5
x
–5
9a. h 7, k 3
9b. 11 3 a(11 7)2
9c. a 11 3 2 8 0.5
16
(11 7)
9d. b y 11 3 8,
y3
2
x 7
a x 11 7 4,
4
8
________ ___
_____ _____
(x 7)2
(x 7)2
9e. y 3 8______
, y 3 8______
16 , y 42
8
__
2
3 16 (x 7) , y 3 0.5(x 7)2; the equations are
equivalent.
10a.
y
5
5
–5
10b.
x
y
5
| _____ |
_____
–5
5
x
–5
10c.
y
5
–5
5
x
–5
11a.
y
–5
6. yˆ 艐 x 18.4. The transmitter is located on the
road approximately 18.4 mi from where you started.
7a. (6, 2)
7b. (2, 3) and (8, 3)
7c. (2, 2) and (8, 2)
5
x
–10
11b.
y
5
5
–5
10
x
–5
44
ANSWERS TO ALL EXERCISES
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y
11c.
14a.
y
5
–5
x
–5
12.
Households (%)
5
55
50
45
40
35
30
x
0
1996
1998
Year
2000
14b. y 4.25x 8447.675
possible equation:
y 1050 x 4 162
_
13a. x 83.75, s 7.45
14c. The model predicts 65.1%, so it overestimates
by 3.3%.
14d. Sample answer: A linear model cannot work to
predict results for years in the distant future because
the percentage cannot increase beyond 100%. There
always will be some households without computers,
so the long-run percentage will be less than 100%.
_
Answers to All Exercises
13b. x 89.75, s 7.45
13c. By adding 6 points to each rating, the mean
increases by 6, but the standard deviation remains the
same.
ANSWERS TO ALL EXERCISES
DAA2TE_985_ANS_a.indd 45
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y3
4e. _____ LESSON 4.7
5
1. See below.
______
2. y 21 x2
y
3a.
or y 5
x 2 2,
_____
2 ___________
x2 2 3
1 _____
1 2
___________
y2
4f. _____ 1 (x 3)2 ,
4 ___________
or y 41 (x 3)2 2
______
5a. y 1 x2 2, or x2 y 22 1
5
–5
___________
5
x
y
5
–5
3b.
y
–5
5
x
5
–5
–5
5
___________
x
5b. y 1 (x 3)2 , or (x 3)2 y2 1
y
–5
3c.
5
y
–5
Answers to All Exercises
5
5
x
–5
–5
5
x
__y 2 1
______
5c. y 21 x 2 , or x2 –5
2
y
______
__y ______
1 x2 , or y 31 x2
3
______
______
y
4b. ___ 1 x2 , or y 0.51 x2
0.5
______
______
y1
4c. _____ 1 x2 , or y 21 x2 1
2
___________
y1
_____
4d.
1 (x 3)2 ,
5
4a.
–5
5
x
–5
2 ___________
or y 21 (x 3)2 1
1. (Lesson 4.7)
Equation
Transformation
(translation, reflection,
dilation)
Direction
Amount
or
scale factor
y ⫹ 3 ⫽ x2
Translation
Vertical
⫺3
⫺y ⫽ x Reflection
Across x-axis
N/A
4
Dilation
Horizontal
4
2
Dilation
Vertical
0.4
Translation
Horizontal
2
Reflection
Across y-axis
N/A
__
y⫽
_x
___y ⫽ x
0.4
y ⫽ x ⫺ 2
___
y ⫽ ⫺x
46
ANSWERS TO ALL EXERCISES
DAA2TE_985_ANS_a.indd 46
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_______
__
__
2
2
5d. y 1 x , or x y2 1
4
2
10a.
10b.
y
y
y
4
2
5
–5
5
3
–2
–2
–4
x
(–3, 0)
(4, 1)
4 6 8
x
__
__
__
___
___
__
___
___
___ ____ __
___
(0, 0) and (1, 1)
9b. The rectangle has width 1 and height 1. The width
is the difference in x-coordinates, and the height is the
difference in y-coordinates.
9c.
(0, 0) and (4, 2)
9d. The rectangle has width 4 and height 2. The width
is the difference in x-coordinates, and the height is the
difference in y-coordinates.
–3
1
x
10d.
y
4
–5
y
_13 , 1
5
–4
x
4
–10
–5
5
(1, –2)
10
x
–4
–8
____
11a. 100
94
11b. Original ratings (from Exercise 13 in Lesson
_
_
4.6): x 83.75, s 7.45. New ratings: x 89.10,
s 7.92.
11c.
100
The scores have been stretched by a factor of ___
94 .
All scores increased, so the mean increased. The
high scores differ from the original by more than the
lower ones, so the scores are more spread out, and the
standard deviation is increased.
11d. Sample answer: The judge should add 6 points
because it does not change the standard deviation.
Everyone gets the same amount added instead of
those with higher scores getting more.
12. 625, 1562.5, 3906.25
13a. a 2.13 or 3.87
13b. b 4 or 8
13c. c 0.2 or 3.8
__
13d. d 1 22 ; d 1.83 or d 3.83
ANSWERS TO ALL EXERCISES
DAA2TE_985_ANS_a.indd 47
Answers to All Exercises
2
6a. x y2 1
3
6b. x
3
6c. g(x) f x
3
2
y
7a. x2 = 1
0.5
2
7b. x y2 1
0.5
2
7c. x (2y)2 1
2
_________
_________
2
2
x
8a. y 3 1 and y 3 1 x 0.5
0.5
_________
2
8b. y 3 1 x 0.5
2
y2
2
8c. y2 9 1 x or x 1
0.5
0.25 9
9a.
–6
–3
10c.
–5
–9
47
3/12/09 8:12:13 PM
16a. y 3x 1
14a, b.
y
y 3x 1
y 3x 1
x
sample answer: yˆ 0.07(x 3)2 21
14c. For the sample answer: residuals: 5.43, 0.77,
0.97, 0.83, 2.63, 0.43, 7.77; s 4.45
14d. approximately 221 ft
14e. 14d should be correct 4.45 ft.
15a, c, d.
16b. y 3x 1
y
y 3x 1
y 3x 1
x
16c. y 3x 1
Answers to All Exercises
Number of airports
y
10
8
6
Mean
4
y 3x 1
y 3x 1
x
2
0
0 30 40 50 60 70 80 90
Number of passengers (in millions)
16d. The two lines are parallel.
15c. mean = 44.67 million
15d. Five-number summary: 32.5, 32.5, 42.5, 52.5,
87.5; assume that all data occur at midpoints of bins.
48
ANSWERS TO ALL EXERCISES
DAA2TE_985_ANS_a.indd 48
3/12/09 8:12:15 PM
9c. g ( f (x)) g (2x 1) _12 (2x 1) _12 x for all x
LESSON 4.8
6
1b. 7
1c. 6
2
2b. 1
2c. 0
approximately 1.5 m/s
approximately 12 L/min
approximately 15 L/min
1d. 18
4a.______
product: f (x) g(x) where f (x) 5 and g(x) __
3
2x
;
composition:
f
(g(x))
where
f(x)
5
x
and g(x) 3 2x
4b. composition: g( f(x)) where f (x) x5
and g(x) 3 (x 3)2
4c. product: f (x) __g(x) where f (x) (x 5)2
and g(x) 2 x
5a. y (x 3)2 1
5b. f (x) x and g(x) (x 3)2 1
C
B
80
60
40
20
40
30
20
10
0
10 20 30 40
A
0
7b. approximately 41
20 40 60 80
B
y
__
__
__ __
y
y
5
5
5
x
–5
13a. x 5 or x 13 13b. x 1 or x 23
___
13c. x 64
13d. x 1.5 1.22
14a. The independent variable, x, is potential
difference (in volts). The dependent variable, y, is
current (in amperes).
14b.
3
7c. possible answer: B 2 (A 12) 13
3
7d. possible answer: C 9 (B 20) 57
4
9
7e. possible answer: C 2 A 5 43
12 1.5A 23.25
8a.
8b.
–5
–5
5
x
–5
2
1
x
3
6
9 12
0
Potential difference (volts)
14c. yˆ 0.2278x 0.0167
14d. yˆ 0.2278x
14e. The ohm rating is the reciprocal of the slope of
this line.
14f. 4.4 ohms
y2
2
15a. x 1, or x2 y2 9
3
3
15b.
__
__
y
8c.
5
(0, 3)
y
5
–5
(–3, 0)
–5
5
x
–5
8d. a. x 2; b. all real numbers; c. all real numbers
9a. 2 9b. 1
(3, 0)
x
5
(0, –3)
–5
16a. g(x) (x 3)2 5
16b. (3, 5)
16c. (1, 9)
ANSWERS TO ALL EXERCISES
DAA2TE_985_ANS_a.indd 49
Answers to All Exercises
6a. 2 6b. 6
6c. The composition of f and g will always give back
the original number because f and g “undo” the effects
of each other.
7a.
9d. f (g(x)) f _12 x _12 2 _12 x _12 1 x for all x
9e. The two functions “undo” the effects of one
another and thus give back the original value.
10a. 4
10b. 3
10c. 3.0625
10d. 4
4
3
2
10e. x 8x 22x 24x 5
10f. x4 4x3 2x2 4x 1
11. If the parent function is y x2, then the equation
______is
y 3x2 3. If the parent function
is
y
1 x2 ,
______
2
then the equation is y 31 x . It appears that
when x 0.5, y 2.6. Substituting 0.5 for x in each
equation gives the following
results:
_______
3(0.5)2 3 2.25 31 0.52 2.598 Thus, the
stretched semicircle is the better fit.
12a. Jen: $4.49; Priya: $4.44
12b. C(x) x 0.50
12c. D(x) 0.90x
12d. C(D(x)) 0.90x 0.50
12e. Priya’s server
12f. There is no price because 0.90x 0.50 0.90(x 0.50) has no solution.
Current (amps)
1a.
2a.
3a.
3b.
3c.
49
3/12/09 8:12:16 PM
5c.
CHAPTER 4 REVIEW
5d.
y
Pops per second
1. Sample answer: For a time there are no pops.
Then the popping rate slowly increases. When the
popping reaches a furious intensity, it seems to level
out. Then the number of pops per second drops
quickly until the last pop is heard.
y
–7
5
5
–5
x
7
–5
–5
5e.
5f.
y
y
3
5
Time (s)
Answers to All Exercises
2a. 1
2b. 7
2c. (x 3)2 3
2d. 7
2e. 1
2f. 100
2g. 2a2 11
2h. 4a2 28a 47
2i. 4a2 32a 64
y
3a.
3b.
x
y
x
7
–3
3d.
y
5
5
x
__
_____
______
2
6b. y 1 x2 ; y 2 1 x 3
5
___________
______
2
6c. y 1 x2 ; y 4 1 x 3 1
4
6d. y x2; y (x 2)2 4
6e. y x2; y 2(x 1)2
________
__
6f. y x ; y (x 2) 3
6g. y x; y 0.5x 2 2
6h. y x; y 2x 3 2
x
–5
4a. Translate horizontally 2 units and vertically
3 units.
4b. Dilate horizontally by a factor of 2, and then
reflect across the x-axis.
4c. Dilate horizontally by a factor of _12 , dilate
vertically by a factor of 2, translate horizontally 1 unit
and vertically 3 units.
5a.
5b.
__
7a. y 2 x 2
3
7b.
7c.
8a.
8c.
8d.
9a.
_____
y x 3 1
_________
y (x 2)2 1
___
x 8.25
8b. x 45 6.7
x 11 or x 5
no solution
17,000 16,000 15,000 14,000 13,000 12,000 11,000 10,000
18,700 19,200 19,500 19,600 19,500 19,200 18,700 18,000
9b.
y
y
4
5
50
______
–5
7
–5
–7
y
–3
x
_______
10
5
7
6a. y 1 x2 ; y 31 x2 1
–5
–5
–3
______
–5
3c.
x
–5
5
5
7
–3
5
–5
x
x
–5
5
–6
x
9c. (1.40, 19,600). By charging $1.40 per ride, the
company achieves the maximum revenue, $19,600.
9d. yˆ 10,000(x 1.4)2 19,600
i $16,000
ii $0 or $2.80
ANSWERS TO ALL EXERCISES
DAA2TE_985_ANS_a.indd 50
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