Answer Key - Mr. Napper's WebPage · 6 • MODULE 2: Exploring Constant Change Module 2, Topic 1 LINEAR FUNCTIONS 9a. 8 9b. 4 9c. 22 9d. All real numbers 9e. All real numbers 10a

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LINEAR FUNCTIONS: Skills Practice Answers • 1

Module 2, Topic 1

LINEAR FUNCTIONS

I. A.1. an 5 16 1 5(n 2 1)

f(n) 5 16 1 5(n 2 1)f(n) 5 16 1 5n 2 5f(n) 5 5n 1 16 2 5f(n) 5 5n 1 11

y

x

8090

706050403020100

2 3 4 5 6 7 81 9

2. an 5 250 1 15(n 2 1)f(n) 5 250 1 15(n 2 1)f(n) 5 250 1 15n 2 15f(n) 5 15n 2 50 2 15f(n) 5 15n 2 65

y

x

6075

453015

–15–30–45

2 3 4 5 6 7 810 9

3. an 5 100 1 (220)(n 2 1)f(n) 5 100 1 (220)(n 2 1)f(n) 5 100 2 20n 1 20f(n) 5 220n 1 100 1 20f(n) 5 220n 1 120

y

x

6080

4020

–20–40–60–80

2 3 4 5 6 7 810 9


y

x–10

–40

–20–30

–50–60–70–80

2 3 4 5 6 7 810 9

Answer Key

IM1_SP_AK_M02_T01.indd 1IM1_SP_AK_M02_T01.indd 1 5/24/18 8:38 PM5/24/18 8:38 PM

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2 • MODULE 2: Exploring Constant Change

Module 2, Topic 1

LINEAR FUNCTIONS


y

x

480540

420360300240180120600

2 3 4 5 6 7 81 9

6. an 5 3 1 (2 3 __ 5 ) (n 2 1)

f(n) 5 3 1 (2 3 __ 5 ) (n 2 1)

f(n) 5 3 2 3 __ 5 n 1 3 __ 5

f(n) 5 2 3 __ 5 n 1 3 1 3 __ 5

f(n) 5 2 3 __ 5 n 1 18 ___ 5

y

x

34

21

–1–2–3–4

2 3 4 5 6 7 810 9

II. A.1. The distance Nathan travels depends on the

time. Distance, D, is the dependent quantity and time, t, is the independent quantity.

D(t) 5 6t

3. The total number of envelopes Mario stuff s depends on the time. The total number of envelopes, E, is the dependent quantity and time, t, is the independent quantity.

E(t) 5 5t

5. The amount of money the booster club earns depends on the number of cups sold. The amount of money, M, is the dependent quantity and the number of cups sold, c, is the independent quantity.

M(c) 5 2c

2. The distance Sophia travels depends on the time. Distance, D, is the dependent quantity and time, t, is the independent quantity.

D(t) 5 3t

4. The total number of goals Shanise scores depends on the number of games she plays. The total number of goals scored, S, is the dependent quantity and the number of games played, g, is the independent quantity.

S(g) 5 4g

6. The amount of money the booster club earns depends on the number of T-shirts sold. The amount of money, M, is the dependent quantity and the number of T-shirts sold, t, is the independent quantity.

M(t) 5 12t


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Module 2, Topic 1

LINEAR FUNCTIONS

II. B.

1. Independent Quantity

Dependent Quantity

Quantity Time Distance

Units hours miles

Expression t 7t

0 0

0.5 3.5

1 7

1.5 10.5

2 14

(0.5, 3.5) and (1, 7)

7 2 3.5 ________ 1 2 0.5 5 3.5 ____ 0.5

5 7 __ 1

The unit rate of change is 7.


Dependent Quantity

Quantity Time Distance

Units hours miles

Expression t 2t

0.25 0.5

0.5 1

1 2

1.25 2.5

1.5 3

(0.25, 0.5) and (0.5, 1)

1 2 0.5 __________ 0.5 2 0.25 5 0.5 _____ 0.25

5 2 __ 1



Dependent Quantity

Quantity Time Number of Envelopes

Units minutes envelopes

Expression t 4t

5 20

10 40

15 60

20 80

25 100

(5, 20) and (10, 40)

40 2 20 ________ 10 2 5 5 20 ___ 5

5 4 __ 1



Dependent Quantity

Quantity Number of Games Played

Total Number of Points Scored

Units games points

Expression g 12g

1 12

3 36

5 60

7 84

9 108

(3, 36) and (5, 60)

60 2 36 ________ 5 2 3 5 24 ___ 2

5 12 ___ 1



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Module 2, Topic 1

LINEAR FUNCTIONS


Dependent Quantity

QuantityNumber of

Bags of Popcorn Sold

Amount of Money Raised

Units bags dollars

Expression b 3b

5 15

10 30

15 45

20 60

25 75

(5, 15) and (10, 30)

30 2 15 ________ 10 2 5 5 15 ___ 5

5 3 __ 1



Dependent Quantity

QuantityNumber of Sweatshirts

SoldAmount of

Money Raised

Units sweatshirts dollars

Expression s 18s

5 90

10 180

20 360

30 540

40 720

(5, 90) and (10, 180)

180 2 90 _________ 10 2 5 5 90 ___ 5

5 18 ___ 1


III. A.

1a. 25 1b. 5 1c. 6

2a. 1 2b. 22 1 __ 3 2c. 22

3a. 5 3b. 5 3c. 5

4a. 21 4b. 11 4c. 22

5a. 4.8 5b. 22.7 5c. 21.2

6a. 15 6b. 9 2 ___ 5 6c. 3

7a. 28 7b. 2

1 __ 2 7c. 0

8a. 3 8b. 6 8c. 0


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Module 2, Topic 1

LINEAR FUNCTIONS

IV. A.

1a. 3 1b. Does not exist 1c. 0 1d. All real numbers 1e. {3}

2a. 4 2b. 2 2c. 22 2d. All real numbers 2e. All real numbers


4a. 4 4b. 16 4c. 2

1 __ 4 4d. All real numbers 4e. All real numbers


6a. 1 6b. 3 6c. 2



8a. 29 8b. 218 8c. 2


9a. 0 9b. 248 9c. 215

10a. 13 ___ 8

10b. 5 __ 8

10c. 1

11a. 1 11b. 299 11c. 11

12a. 7 12b. 233 12c. 218


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Module 2, Topic 1

LINEAR FUNCTIONS


10a. 8 10b. 216 10c. 1 __ 2 10d. All real numbers 10e. All real numbers

11a. 9 11b. 12 11c. 2



V. A.

1.

−8 −6 −4 −2−2

−4

20 4

p(x)

f(x)

6 8

−8

−6

8

6

4

2

y

x

Original Graph Transformed Graph

x f(x) x p(x)

22 22 22 29

21 21 21 28

0 0 0 27

1 1 1 26

2 2 2 25


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Module 2, Topic 1

LINEAR FUNCTIONS

2.

−8 −6 −4 −2−2

−4

20 4

p(x)

f(x)

6 8

−8

−6

8

6

4

2

y

x


x f(x) x p(x)

22 22 22 2

21 21 21 3

0 0 0 4

1 1 1 5

2 2 2 6

3.

−8 −6 −4 −2−2

−4

20 4

p(x)f(x)

6 8

−8

−6

8

6

4

2

y

x


x f(x) x p(x)

22 22 22 6

21 21 21 7

0 0 0 8

1 1 1 9

2 2 2 10


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Module 2, Topic 1

LINEAR FUNCTIONS

4.

−8 −6 −4 −2−2

−4

20 4

p(x)

f(x)

6 8

−8

−6

8

6

4

2

y

x


x f(x) x p(x)

22 22 22 24

21 21 21 23

0 0 0 22

1 1 1 21

2 2 2 0

5.

−8 −6 −4 −2−2

−4

20 4

p(x)

f(x)

6 8

−8

−6

8

6

4

2

y

x


x f(x) x p(x)

22 22 22 27

21 21 21 26

0 0 0 25

1 1 1 24

2 2 2 23


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Module 2, Topic 1

LINEAR FUNCTIONS

6.

−8 −6 −4 −2−2

−4

20 4

p(x)

f(x)

6 8

−8

−6

8

6

4

2

y

x


x f(x) x p(x)

22 22 22 5 __ 2

21 21 21 7 __ 2

0 0 0 9 __ 2

1 1 1 11 ___ 2

2 2 2 13 ___ 2

V. B. 1. g(x) 5 f(x) 1 9

5 3x 1 1 1 9 5 3x 1 10

2. g(x) 5 f(x) 2 13 5 6x 2 10 2 13 5 6x 2 23

3. g(x) 5 f(x) 1 21 5 27 2 4x 1 21 5 24x 1 14

4. g(x) 5 f(x) 2 12 5 22x 2 7 2 12 5 22x 2 19

5. g(x) 5 f(x) 2 4

5 1 __ 2 x 1 2 2 4

5 1 __ 2 x 2 2

6. g(x) 5 f(x) 1 16 5 3 2 5x 1 16 5 25x 1 19


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Module 2, Topic 1

LINEAR FUNCTIONS

V. C.1.

−8 −6 −4 −2−2

−4

20 4

m(x)

f(x)

6 8

−8

−6

8

6

4

2

y

x


x f(x) x m(x)

22 22 22 210

21 21 21 25

0 0 0 0

1 1 1 5

2 2 2 10

2.

−8 −6 −4 −2−2

−4

20 4

m(x)

f(x)

6 8

−8

−6

8

6

4

2

y

x


x f(x) x m(x)

22 22 212 22

21 21 26 21

0 0 0 0

1 1 6 1

2 2 12 2


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Module 2, Topic 1

LINEAR FUNCTIONS

3.

−8 −6 −4 −2−2

−4

20 4

m(x)

f(x)

6 8

−8

−6

8

6

4

2

y

x


x f(x) x m(x)

22 22 22 2 1 __ 3

21 21 21 2 1 __ 6

0 0 0 0

1 1 1 1 __ 6

2 2 2 1 __ 3

4.

−8 −6 −4 −2−2

−4

20 4

m(x)

f(x)

6 8

−8

−6

8

6

4

2

y

x


x f(x) x m(x)

24 24 22 24

22 22 21 22

0 0 0 0

2 2 1 2

4 4 2 4


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Module 2, Topic 1

LINEAR FUNCTIONS

5.

−8 −6 −4 −2−2

−4

20 4

m(x)

f(x)

6 8

−8

−6

8

6

4

2

y

x


x f(x) x m(x)

22 22 22 26

21 21 21 23

0 0 0 0

1 1 1 3

2 2 2 6

6.

−8 −6 −4 −2−2

−4

20 4

m(x)f(x)

6 8

−8

−6

8

6

4

2

y

x


x f(x) x m(x)

24 24 24 23

22 22 22 2 3 __ 2

0 0 0 0

2 2 2 3 __ 2

4 4 4 3


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Module 2, Topic 1

LINEAR FUNCTIONS

V. D. 1. The graph of the function f(x) is translated

down 8 units to produce g(x).

−8 −6 −4 −2−2

−4

20 4

g(x)

f(x)

6 8

−8

−6

8

6

4

2

y

x

3. The graph of the function f(x) is translated up 5 units to produce g(x).

−8 −6 −4 −2−2

−4

20 4

g(x)

f(x)

6 8

−8

−6

8

6

4

2

y

x

2. The graph of the function f(x) is stretched vertically by a factor of 2 to produce g(x).

−8 −6 −4 −2−2

−4

20 4

g(x)

f(x)

6 8

−8

−6

8

6

4

2

y

x

4. The graph of the function f(x) is compressed vertically by a factor of 2 __ 3 to produce g(x).

−8 −6 −4 −2−2

−4

20 4

g(x)f(x)

6 8

−8

−6

8

6

4

2

y

x


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Module 2, Topic 1

LINEAR FUNCTIONS

5. The graph of the function f(x) is translated down 4 units to produce g(x).

−8 −6 −4 −2−2

−4

20 4

g(x)

f(x)

6 8

−8

−6

8

6

4

2

y

x

6. The graph of the function f(x) is stretched vertically by a factor of 4 to produce g(x).

−8 −6 −4 −2−2

−4

20 4

g(x)

f(x)

6 8

−8

−6

8

6

4

2

y

x

VI. A. 1. y 5 4 __ 5 x 1 6 __ 5

2. y 5 25x 1 16

3. y 5 7x 2 37

4. y 5 2 1 __ 2 x 2 1

5. y 5 1 __ 3 x 1 5

6. y 5 24x 2 1

VI. C. 1. x 5 22

2. x 5 3

3. x 5 9

4. x 5 211

5. x 5 25

6. x 5 0

VI. B. 1. y 5 2 1 __ 2 x 1 13 ___ 2

2. y 5 1 __ 3 x 1 19 ___ 3

3. y 5 5 __ 2 x 2 13

4. y 5 2 4 __ 3 x 1 19

5. y 5 2 1 __ 6 x 2 2

6. y 5 2 2 __ 5 x 2 22 ___ 5

VI. D. 1. y 5 7

2. y 5 5

3. y 5 23

4. y 5 29

5. y 5 8

6. y 5 22


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Module 2, Topic 1

LINEAR FUNCTIONS

VII. A.

1a. The rate of change for Oscar’s distance is 1. This means he jumps 1 more inch each month. The rate of change for Monica’s distance is 1. This means she jumps 1 more inch each month. They are both increasing their distances at the same rate.

1b. The y-intercept for Oscar’s distances is 235. This means that he jumped 235 inches at the beginning of the track season. The y-intercept for Monica’s distances is 200. This means that she jumped 200 inches at the start of the season. Oscar jumped further at the beginning of the track season than Monica.

2a. The rate of change for Tremaine’s distance is 60. This means he is traveling 60 miles per hour. The rate of change for Jose’s speed is 55. This means he is traveling 55 miles per hour. Tremaine is driving at a faster rate.

2b. The y-intercept for Tremaine’s distance is 0. This means that he starts the trip in L.A. The y-intercept for Jose’s distances is 2100. This means that he was 100 miles away from L.A. before he started his trip to San Francisco.

3a. The rate of change for Alyssa’s net earnings is 45. This means she earns $45 for each lawn she mows. The rate of change for Matsuo’s net earnings is 30. This means he earns $30 for each lawn he mows. Alyssa earns more per lawn than Matsuo.

3b. The y-intercept for Alyssa’s net earnings is 2250. This means the lawn mower cost her $250. The y-intercept for Matsuo’s net earnings is 2200. This means the lawn mower cost him $200.

4a. The rate of change for Concepcion’s debt is 2800. This means he is paying his grandmother back $800 a month. The rate of change for Marian’s debt is 2400. This means she is paying her grandmother back $400 a month. Concepcion is paying more per month than Marian.

4b. The y-intercept for Concepcion’s debt is 25,000. This means she initially borrowed $25,000 from her grandmother. The y-intercept for Marian’s debt is 10,000. This means she initially borrowed $10,000 from her grandmother.

5a. The rate of change for Marcus’s account balance is 125. This means he is saving $125 each month. The rate of change for Belita’s account balance is 100. This means she is saving $100 each month. Marcus is saving more per month than Belita.

5b. The y-intercept for Marcus’s account balance is 300. This means he started with $300 in his account. The y-intercept for Belita’s account balance is 225. This means she started with $225 in her account.


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Module 2, Topic 1

LINEAR FUNCTIONS

6a. The rate of change for Orpheus’s distance is 50. This means he is driving 50 miles per hour. The rate of change for Louis’s distance is 65. This means he is driving 65 miles per hour. Louis is driving at a faster rate than Orpheus.

6b. The y-intercept for Orpheus’s distance is 0. This means he started in Harrisburg. The y-intercept for Louis’s distance is 150. This means he was 150 miles away from Harrisburg when Orpheus left Harrisburg.

7a. The rate of change for The Pavilion’s line is 10. This means The Pavilion lets in 10 people every hour. The rate of change for Heliophobia’s line is 15. This means Heliophobia lets in 15 people every hour. Heliophobia is letting in more people per hour than The Pavillion.

7b. The y-intercept for The Pavilion’s line is 50. This means initially the arcade let 50 people in. The y-intercept for Heliophobia’s line is 70. This means initially the arcade let 70 people in.

8a. The rate of change for Henry’s account balance is 75. This means he is saving $75 each month. The rate of change for Walter’s account balance is 75. This means he is saving $75 each month. They are saving the same amount of money per month.

8b. The y-intercept for Henry’s account balance is 600. This means he started with $600 in his account. The y-intercept for Walter’s account balance is 175. This means he started with $175 in his account.

9a. The rate of change for Susan’s debt is 2600. This means she is paying her parents back $600 a month. The rate of change for Caitlin’s debt is 2800. This means she is paying her parents back $800 a month. Caitlin is paying more per month than Susan.

9b. The y-intercept for Susan’s debt is 45,000. This means she initially borrowed $45,000 from her parents. The y-intercept for Caitlin’s debt is 35, 000. This means she initially borrowed $35,000 from her parents.

10a. The rate of change for the number of red velvet cupcakes sold is 20. This means the bakery sells 20 red velvet cupcakes per hour. The rate of change for the number of almond croissants sold is 30. This means the bakery sells 30 almond croissants per hour. The bakery is selling more almond croissants per hour than red velvet cupcakes.

10b. The y-intercept for the number of red velvet cupcakes sold is 125. This means the bakery sold 125 cupcakes right when they opened. The y-intercept for the number of almond croissants sold is 125. This means the bakery sold 125 croissants right when they opened.


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Module 2, Topic 1

LINEAR FUNCTIONS

11a. The rate of change for the Youth Division’s distance from the fi nish line is 2235. This means the distance is decreasing by 235 meters per minute. The rate of change for the Masters Division’s distance from the fi nish line is 2240. This means the distance is decreasing by 240 meters per minute. The Masters Division is decreasing the distance at a faster rate than the Youth Division.

11b. The y-intercept for the Youth Division’s distance from the fi nish line is 2910. This means the Youth Division started the race 2910 meters away from the fi nish line. The y-intercept for the Masters Division’s distance from the fi nish line is 3000. This means the Masters Division started the race 3000 meters away from the fi nish line.

12a. The rate of change for the line at Dave’s Games is 8. This means the number of people in line increases by 8 each minute. The rate of change for the line at Hum Electronics is 13. This means the number of people in line increases by 13 each minute. The line at Hum Electronics is growing at a faster rate than the line at Dave’s Games.

12b. The y-intercept for the line at Dave’s Games is 65. This means there were 65 people in line before they opened. The y-intercept for the line at Hum Electronics is 80. This means there were 80 people in line before they opened.


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Answer Key - Mr. Napper's WebPage · 6 • MODULE 2: Exploring Constant Change Module 2, Topic 1 LINEAR FUNCTIONS 9a. 8 9b. 4 9c. 22 9d. All real numbers 9e. All real numbers 10a