answers to all exercises - weeblymissbuckles.weebly.com/uploads/2/2/4/6/22466700/daa_te_ch04.pdf ·...

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34 ANSWERS TO ALL EXERCISES

CHAPTER 4 • CHAPTER CHAPTER 4 • CHAPTER 4REFRESHING YOUR SKILLS FOR CHAPTER 4

1a. Add 7 to each side.

1b. Multiply each side by 1 _ 3 or divide each side by 3.

1c. Add �2 to each side or subtract 2 from each side.

1d. Square each side.

1e. Add �6 to each side or subtract 6 from each side.

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.

Answers to All Exercises

DAA2TE_985_ANS_a.indd 34DAA2TE_985_ANS_a.indd 34 3/12/09 9:44:01 PM3/12/09 9:44:01 PM

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ANSWERS TO ALL EXERCISES 35

LESSON 4.1

1a. A 1b. C 1c. D 1d. B

2a. 2b. 2c.

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 indep endent variable; the height of the ball in feet is the dependent variable.

Time (s)

Hei

ght (

ft)

6b. The car’s speed in miles per hour is the independent variable; the braking distance in feet is the dependent variable.

Speed (mi/h)

Bra

kin

gd

ista

nce

(ft

)

6c. Time in minutes is the independent variable; the drink’s temperature in degrees Fahrenheit is the dependent variable.

Time (min)

Tem

per

atu

re (

°F)

6d. Time in seconds is the independent variable; the acorn’s speed in feet per second is the dependent variable.

Time (s)

Spee

d (

ft/s

)

6e. Time in minutes is the independent variable; your height above the ground in feet is the depen-dent variable.

Time (min)

Hei

ght (

ft)

7a. Time in years is the independent variable; the amount of money in dollars is the dependent vari-able. The graph will be a series of discontinuous segments.

Time (yr)

Am

oun

t ($)

7b. Time in years is the independent variable; the amount of money in dollars is the dependent vari-able. The graph will be a continuous horizontal segment, because the amount never changes.

Time (yr)

Am

oun

t ($)


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7c. Foot length in inches is the independent vari-able; shoe size is the dependent variable. The graph will be a series of discontinuous horizontal segments, because shoe sizes are discrete.

Foot length (in.)

Shoe

siz

e

7d. Answers will vary but should be in the form of a discrete graph.

Day of the month

Pri

ce p

er g

allo

n

7e. The day of the month is the independent vari-able; the maximum temperature in degrees Fahr-enheit is the dependent variable. The graph will be discrete points, because there is just one tempera-ture reading per day.

Day of the month

Max

imu

m te

mp

erat

ure

(°F

)

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

Time (h)

Cos

t ($)

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.

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

2Number of pictures

Am

oun

t of

mon

ey (

$)

4 6 8 10 12 14 16

80

160

240

400

320

y

x

Cost: y � 155 � 15x

Income: y � 27x

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


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LESSON 4.2

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 2c. �19

2d. 11 2e. 11 ___ 3

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.

5b. The time the money has been in the bank is the inde pendent 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 fill-up 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.

x

y

6b. Let x represent the time in months, and let y represent the account balance in dollars.

x

y

6c. Let x represent the time in days, and let y represent the length of your hair.

x

y

6d. Let x represent the distance you have driven in miles, and let y represent the amount of gasoline in your tank in gallons.

x

y

7a, c, d.

x

y

–25 25

–25

(–4, 27.4) (7, 20.8)

7b. 20.8 7d. �4

8. domain: �6 � x � 5; range: �2 � y � 4

9a. possible answer:

x

y

9b. possible answer: 9c.

x

y

x

y

10a. 104

10b. f (n) � 3(n � 1)2 � 4

10c. f (x � 2) � 3(x � 3)2 � 4

10d.

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


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14a.

Time

Hei

ght

14b.

Time

Hei

ght

14c.

Time

Hei

ght

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)


x

f(x)

17b. possible answer:

x

f(x)

10–10

–3

3

17c. possible answer:

x

f(x)

–2

10

18a. 18b.

3x

x

7

x2 3x

7x 21

x2 x

2x 2

x 1

x

2

18c.

2x2 10x

20x 100

2x 10

x

10

19a.y

x1 2

Dis

tan

ce (

m)

Time (s)3 4 5 6

5

0

1

2

3

4(4, 2.2)

C(t) � 0.2 � 0.5x

A(t) � 4.2 � 0.5x

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.


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LESSON 4.3

1. y � �3 � 2 __ 3 (x � 5)

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

4a. y � �4.4 � 1.1 __

48 (x � 1.4) or y � 3.18 � 1.1

__ 48 (x � 5.2)

4b. y � �2.4 � 1.1 ___

48 (x � 1.4) or y � 5.18 � 1.1

__ 48 (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 __ b

� a __ b

x; y-intercept: c __ b

; slope: � a __ b

10c. i. y-intercept: 4; slope: � 4 _ 3

10c. ii. y-intercept: 5; slope: 1

10c. iii. y-intercept: �1; slope: 7

10c. iv. y-intercept: � 1 _ 2 ; slope: 1 _ 2

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

12a. 80.8

12b. y � 1 __ 5 x � 65

12c. 95 points

13a. x � 15

13b. x � 31

13c. x � �21

13d. x � 17.6

14. y � 29 ___ 2 � 3 __ 2 x


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LESSON 4.4

1a. y � x 2 � 2

1b. y � x 2 � 6

1c. y � (x � 4) 2

1d. y � (x � 8) 2

2a. y � x 2 � 5

x

y

–5 5

–5

5

2b. y � x 2 � 3

x

y

–5 5

–5

5

2c. y � (x � 3) 2

x

y

–5 5

–5

5

2d. y � (x � 4) 2

x

y

–5 5

–5

5

3a. translated vertically �3 units

3b. translated vertically 4 units

3c. translated horizontally 2 units

3d. translated horizontally �4 units

4a. translated horizontally 3 units

4b. translated horizontally �3 units

4c. translated vertically 2 units

4d. translated vertically �2 units

5a. x � 2 or x � �2

5b. x � 4 or x � �4

5c. x � 7 or x � �3

6a. y � (x � 2) 2

6b. y � (x � 2) 2 �5

6c. y � (x � 6) 2

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.

x

y

5

–5

5

8b.

x

y

5–5

–5

5

9a.

Number of

teams (x ) 4 5 6 7 8 9 10

Number of

games ( y ) 12 20 30 42 56 72 90

9b. The points appear to be part of a parabola.

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


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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.

m

C

2432

51

100 150 190

Luxury

Mertz

Saver

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.

14.

Time

Dis

tan

ce

AC

D

E

X

B

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.


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LESSON 4.5

1a. y � � __

x � 3 1b. y � � _____

x � 5

1c. y � � _____

x � 5 � 2 1d. y � � _____

x � 3 � 1

1e. y � � _____

x � 1 � 4

2a. translated horizontally 3 units

2b. translated horizontally �3 units

2c. translated vertically 2 units

2d. translated vertically �2 units

3a. iii

3b. i

3c. ii

4a. 4b.

x

y

5–5

–5

5

y � f(�x)

x

y

5–5

–5

5

y � �f(x)

4c.

x

y

5–5

–5

5

y � �f(�x)

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

6c. y � � � _____

x � 2 � 3

7a. y � � __

x and y � � � __

x

7b. y � � __

x ; y 2 � x

8a. Neither parabola passes the vertical line test.

8b. i. y � � _____

x � 4

8b. ii. y � � __

x � 2

8c. i. y 2 � x � 4

8c. ii. (y � 2) 2 � x


x

y

Time (h)

Dis

tan

ce (

mi)

0

50

100

150

200

250

2 4 6 8

ArthurJake

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 � 5.5 � _____

0.7D

13b.

D

S

13c. approximately 36 mi/h

13d. D � 1 ___ 0.7 � S

___ 5.5 � 2 ; the minimum braking distance, when the speed is known

13e.


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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

16. y � (x � 6) 2 � 4

17a. y � 1 __ 2 x � 5

17b. y � 1 __ 2 (x � 8) � 5

y

x(–8, 1)

(0, 1)

(2, 6)

(10, 6)

17c. y � � 1 __ 2 x � 5 � � 4, or y � 4 � 1 __ 2 x � 5

17d. Both equations are equivalent to y � 1 __ 2 x � 1.

18a. 35, 37.5, 41.5, 49, 73

18b.

35 40 45 50 55 7560 65 70

18c. 11.5

18d. 70 and 73

19. (8, 7)


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LESSON 4.6

1a. y � �x� � 2

1b. y � �x� � 5

1c. y � �x � 4�1d. y � �x � 3�1e. y � �x� � 1

1f. y � �x � 4� � 1

1g. y � �x � 5� � 3

1h. y

__ 3

� �x � 6�, or y � 3�x � 6�1i. y � � | x __ 4 | 1j. y � (x � 5) 2

1k. �2y � �x � 4�, or y � � 1 __ 2 �x � 4�1l. y � ��x � 4� � 3

1m. y � �(x � 3) 2 � 5

1n. y � � _____

x � 4 � 3

1p. y ___

�2 � | x � 3 _____ 3 | , or y � �2 | x � 3 _____ 3 | 2a. horizontal dilation by a factor of 3

2b. reflection across the y-axis

2c. horizontal dilation by a factor of 1 _ 3

2d. vertical dilation by a factor of 2

2e. reflection across the x-axis

2f. vertical dilation by a factor of 1 _ 2

3a. y � 2(x � 5) 2 � 3

3b. y � 2 | x � 1 _____ 3 | � 5

3c. y � �2 � _____

x � 6 _____ � 3 � 7

4. For b � 0, the graphs of y � b�x� and y � �bx� are equivalent. For b 0, the graph of y � b�x� is a reflection of y � �bx� across the x-axis.

5a. 1 and 7; x � 1 and x � 7

5b. x � �8 and x � 2

6. y � �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)

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.

x

y

–5

5

9a. h � 7, k � 3 9b. 11 � 3 � a(11 � 7) 2

9c. a � 11 � 3 ________ (11 � 7) 2

� 8 ___ 16 � 0.5

9d. b � �y � 11 � 3 � 8,

a � �x � 11 � 7 � 4, y � 3

_____ 8 � � x � 7 _____ 4 � 2

9e. y � 3 � 8 (x � 7) 2

______ 4 2

, y � 3 � 8 (x � 7) 2

______ 16 , y �

3 � 8 __ 16 (x � 7) 2 , y � 3 � 0.5(x � 7) 2 ; the equations are equivalent.

10a.

x

y

–5 5

5

10b.

x

y

–5 5

–5

5

10c.

x

y

–5 5

–5

5

11a. x

y

5–5

–10

11b.

x

y

5–5

–5

5

10


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11c.

x

y

5–5

–5

5

12.

possible equation: y � 1050 �x � 4� � 162

13a. _

x � 83.75, s � 7.45

13b. _

x � 89.75, s � 7.45

13c. By adding 6 points to each rating, the mean increases by 6, but the standard deviation re mains the same.

14a.

Year

Hou

seh

old

s (%

)

1996 1998 2000

30

0

35

40

45

50

55

y

x

14b. y � 4.25x � 8447.675

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%.


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LESSON 4.7

1. See below.

2. y � 2 � ______

1 � x 2

3a.

x

y

–5 5

–5

5

3b.

x

y

–5 5

–5

5

3c.

x

y

–5 5

–5

5

4a. y

__ 3 � � ______

1 � x 2 , or y � 3 � ______

1 � x 2

4b. y

___ 0.5 � � ______

1 � x 2 , or y � 0.5 � ______

1 � x 2

4c. y � 1

_____ 2 � � ______

1 � x 2 , or y � 2 � ______

1 � x 2 � 1

4d. y � 1

_____ 2 � � ___________

1 � (x � 3) 2 ,

or y � 2 � ___________

1 � (x � 3) 2 � 1

4e. y � 3

_____ �5 � �

___________

1 � � x � 2 _____ 2 � 2 ,

or y � �5 � ___________

1 � � x � 2 _____ 2 � 2 � 3

4f. y � 2

_____ 4 � � ___________

1 � (x � 3) 2 ,

or y � 4 � ___________

1 � (x � 3) 2 � 2

5a. y � � � ______

1 � x 2 � 2, or x 2 � � y � 2 � 2 � 1

x

y

–5 5

–5

5

5b. y � � � ___________

1 � (x � 3) 2 , or (x � 3) 2 � y 2 � 1

x

y

–5 5

–5

5

5c. y � �2 � ______

1 � x 2 , or x 2 � � y __ 2 � 2 � 1

x

y

–5 5

–5

5

Transformation Amount (translation, reflection, orEquation dilation) Direction scale factor

y � 3 � x2 Translation Vertical �3

�y � � x �

y � � __

x _ 4

y ___ 0.4 � x2

y � � x � 2 �

y � � ___

�x

Reflection Across x-axis N/A

Dilation Horizontal 4

Dilation Vertical 0.4

Translation Horizontal 2

Reflection Across y-axis N/A

1. (Lesson 4.7)

DAA2TE_985_ANS_a.indd 46DAA2TE_985_ANS_a.indd 46 3/30/09 11:54:11 AM3/30/09 11:54:11 AM

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5d. y � � _______

1 � � x __ 2 � 2 , or x 2 __ 4 � y 2 � 1

x

y

–5 5

–5

5

6a. � x __ 3 � 2 � y 2 � 1

6b. x __ 3

6c. g(x) � f � x __ 3 �

7a. x 2 � � y ___ 0.5 �

2 = 1

7b. � x ___ 0.5 � 2 � y 2 � 1

7c. � x __ 2 � 2 � (2y) 2 � 1

8a. y � 3 � _________

1 � � x ___ 0.5 � 2 and y � �3 � _________

1 � � x ___ 0.5 � 2

8b. y � 3 � _________

1 � � x ___ 0.5 � 2

8c. y 2 � 9 � 1 � � x ___ 0.5 � 2 or x 2 ____ 0.25 � y 2

__ 9 � 1

9a.

(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.

10a. 10b.

x

y

–2 84 6

–4

–2

4

2 (4, 1)

x

y

–3–6–9 1

–3

3(–3, 0)

10c. 10d.

x–5–10 5 10

–4

–8

4

y

(1, –2)

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.

The scores have been stretched by a factor of 100 ___ 94 .

All scores in creased, 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 2 � __

2 ; d � 1.83 or d � �3.83

x–5 5

–4

4

y

1_3

, 1� �x

–5 5

–4

4

y

1_3

, 1� �


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14a, b.

sample answer: y � 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.

300 40 50 60 80 9070

Nu

mb

er o

f ai

rpor

ts

2

0

4

6

8

10

Number of passengers (in millions)

Mean

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.

16a. y � �3x � 1

x

y

y � 3x � 1y � �3x � 1

16b. y � �3x � 1

x

y

y � 3x � 1y � �3x � 1

16c. y � 3x � 1

x

y

y � 3x � 1

y � 3x � 1

16d. The two lines are parallel.


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LESSON 4.8

1a. 6 1b. 7 1c. 6 1d. 18

2a. 2 2b. 1 2c. 0

3a. approximately 1.5 m/s

3b. approximately 12 L/min

3c. approximately 15 L/min

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) � �x�5� 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

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.

A

B

10 20 30 40

10

0

20

30

40

B

C

20 40 60 80

20

0

40

60

80

7b. approximately 41

7c. possible answer: B � 2 __ 3 (A � 12) � 13

7d. possible answer: C � 9 __ 4 (B � 20) � 57

7e. possible answer: C � 9 __ 4 � 2 __ 3 A � 5 � � 12 � 1.5A � 23.25

8a. 8b.

x

y

–5 5

–5

5

x

y

–5 5

–5

5

8c.

x

y

–5 5

–5

5

8d. a. x � �2; b. all real numbers; c. all real numbers

9a. 2 9b. �1

9c. g ( f (x)) � g (2x � 1) � 1 _ 2 (2x � 1) � 1 _ 2 � x for all x

9d. f (g(x)) � f � 1 _ 2 x � 1 _ 2 � � 2 � 1 _ 2 x � 1 _ 2 � � 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

10e. �x 4 � 8x 3 � 22x 2 � 24x � 5

10f. x 4 � 4x 3 � 2x 2 � 4x � 1

11. If the parent function is y � x 2 , then the equation is y � �3x 2 � 3. If the parent function is y � �

______ 1 � x 2 ,

then the equation is y � 3 � ______

1 � x 2 . 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 3 �

_______ 1 � 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.

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.y

x

Potential difference (volts)

Cu

rren

t (am

ps)

0

1

2

3

3 6 9 12

14c. y � 0.2278x � 0.0167 14d. y � 0.2278x

14e. The ohm rating is the reciprocal of the slope of this line.

14f. 4.4 ohms

15a. � x __ 3 � 2 � � y __ 3 � 2 � 1, or x 2 � y 2 � 9

15b.

x

y

–5

(–3, 0) (3, 0)

(0, 3)

(0, –3)

5

–5

5

16a. g(x) � (x � 3) 2 � 5

16b. (�3, 5)

16c. (�1, 9)


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CHAPTER 4 REVIEW

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.

Time (s)

Pop

s p

er s

econ

d

2a. �1

2b. 7

2c. (x � 3) 2 � 3

2d. �7

2e. �1

2f. 100

2g. �2a 2 � 11

2h. 4a 2 � 28a � 47

2i. 4a 2 � 32a � 64

3a.

x

y

5–5

–5

5

3b.

x

y

7–3

–5

5

3c.

x

y

5–5

10

3d.

x

y

5–5

–5

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 1 _ 2 , dilate vertically by a factor of 2, translate hori zon tally 1 unit and vertically 3 units.

5a. 5b.

x

y

7–3

–5

5

x

y

5–5

–6

4

5c. 5d.

x

y

5–5

–5

5

x

y

–5

–7 7

5e. 5f.

x

y

7–3

–5

5

x

y

7–3

–7

3

6a. y � � ______

1 � x 2 ; y � 3 � ______

1 � x 2 � 1

6b. y � � ______

1 � x 2 ; y � 2 � _______

1 � � x __ 5 � 2 � 3

6c. y � � ______

1 � x 2 ; y � 4 � ___________

1 � � x � 3 _____ 4 � 2 � 1

6d. y � x 2 ; y � (x � 2) 2 � 4

6e. y � x 2 ; y � �2(x � 1) 2

6f. y � � __

x ; y � � � ________

�(x � 2) � 3

6g. y � �x�; y � 0.5�x � 2� � 2

6h. y � �x�; y � �2�x � 3� � 2

7a. y � 2 __ 3 x � 2

7b. y � � _____

x � 3 � 1

7c. y � � _________

�(x � 2) 2 � 1

8a. x � 8.25 8b. x � � ___

45 � 6.7

8c. x � 11 or x � �5

8d. no solution

9a.

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.

9c. (1.40, 19,600). By charging $1.40 per ride, the company achieves the maximum revenue, $19,600.

9d. y � �10,000(x � 1.4) 2 � 19,600

i $16,000

ii $0 or $2.80


answers to all exercises - weeblymissbuckles.weebly.com/uploads/2/2/4/6/22466700/daa_te_ch04.pdf ·...

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