lesson 10 - drauden point middle schooldpms.psd202.org/documents/ppotock1/1509025881.pdfpractice...

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Practice Lesson 10 Graphs of Functional Relationships

Unit 2

Practice and Prob

lem Solvin

gU

nit 2 Functions

Key

B Basic M Medium C Challenge

©Curriculum Associates, LLC Copying is not permitted. 103Lesson 10 Graphs of Functional Relationships

Name: Graphs of Functional Relationships

Lesson 10

Prerequisite: Compare Rates of Change

Study the example problem showing ways to compare functions. Then solve problems 1–6.

Example

Carmen buys a new bicycle Her weekly payment plan is shown in the table Sam also buys a new bicycle His weekly payment plan is shown in the graph Find the rate of change for each function and explain what it represents

Week 0 1 2 3 4

Amount Carmen Owes ($)

200 150 100 50 0

The amount Carmen owes decreases by $50 each week, so her rate of change is 2$50

The amount Sam owes decreases by $25 each week, so his rate of change is 2$25

Carmen pays more per week than Sam

1 Graph Carmen’s function on the same grid as Sam’s function Which line is steeper?

2 How does the graph show that the rate of change is negative?

3 Suppose Sam decides to pay for his bicycle in two equal weekly payments How would that aff ect his rate of change? Would Sam pay more or less than Carmen each week?

Am

ount

Ow

ed ($

)

Sam’s Payment Plan

Weeks2 4 6 8 91 3 5 7O

x

y

50

25

100

150

175

200

225

75

125

103103

M

Carmen’s line is steeper than Sam’s.

B

Possible explanation: As the x-values of each function increase, the y-values decrease. So,

the lines slant downward from left to right.

Sam’s rate of change would become 2$62.50 instead of 2$25. Sam would pay more than

Carmen each week.

M

©Curriculum Associates, LLC Copying is not permitted.104 Lesson 10 Graphs of Functional Relationships

Solve.

4 Hector wants to buy a new computer monitor The prices and payment options are diff erent at two stores Which store plan has a greater monthly payment? Explain

Store A Payment Plan

Price of $250 Pay $100 at the time of purchase Pay $50 per month until the monitor is paid for

5 Katia and Adam are both taking a 200-mile road trip Their driving speeds are shown below

Mile

s D

rive

n

Katia’s Speed

Hours2 41 3 5O

x

y

80

40

160

120

200

Mile

s D

rive

n

Adam’s Speed

Hours2 41 3 5O

x

y

80

40

160

120

200

Which driver has the greater rate of change? What does this mean in the context of the problem?

6 Look at the graphs in problems 4 and 5 Which graphs have a positive rate of change? Which graphs have a negative rate of change? Explain how you know

Am

ount

Ow

ed ($

)

Store B Payment Plan

Months2 4 6 8 91 3 5 7O

x

y

50

25

100

150

175

200

225

75

125

104

M

Store A has a greater monthly payment of $50.

The rate of change for Store B is 225, so the

monthly payment is $25.

M

M

Adam has the greater rate of change. This means that he is driving at a greater

speed than Katia.

Possible explanation: The graphs in problem 5 have a positive rate of change because the

lines slant upward from left to right. The graph in problem 4 has a negative rate of change

because the line slants downward from left to right.

40

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urricu

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Associates, L

LC

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opying is n

ot permitted.

Practice and Prob

lem Solvin

gU

nit 2 Functions

Unit 2



Name: Lesson 10

Describe Qualitative Graphs

Study the example problem showing how to interpret a qualitative graph. Then solve problems 1–7.

1 Explain how the graph in the example shows that the temperature increases at the beginning of the day What do you know about the slope of the line?

2 Explain how the graph in the example shows that the temperature stays constant for a while

3 This graph shows the speed of a car on a city street Describe and interpret section C of the graph

Time

Spee

d

A

B

C

D

Example

The graph shows the temperature for a day in a city Summarize what the graph shows

The temperature increases at the beginning of the day It stays constant during the middle of the day Then it decreases for the rest of the day

Vocabularyqualitative graph a

graph that represents a

function visually, not

with exact numbers

Time

Dis

tanc

e

Time

Tem

pera

ture

105

B

Possible answer: The line in the first part of the graph is gradually going up. It has a

positive slope.

B

Possible answer: The line in the second part of the graph is a horizontal line.

Possible answer: The car is not moving, so it could

have stopped at a stop sign or traffic light.

M


Solve.

4 Summarize the graph showing the speed of a roller coaster

5 Suppose the label Speed in the graph for problem 4 is changed to Height Explain how that would change your summary of the graph Write a revised summary

6 This graph shows Raj’s distance from school as he walks home at the end of the day Describe what could be happening during each section of the graph

7 This graph shows the weight of a puppy over a 6-month period Tamara says that the puppy’s weight increased at a greater rate at the beginning of the 6-month period than at the end Do you agree? Explain

Time

Spee

d

Time

Dis

tanc

e fr

om S

choo

l

A C

BD

Time

Wei

ght

106

M

C

Possible answer: The speed starts at 0 and gradually

increases. The speed decreases as the roller coaster goes up a

hill and then increases as it comes down the hill. The speed

gradually decreases to 0 as the roller coaster comes to a stop.

M

Possible answer: Section A: He begins walking home from

school. Section B: He stops to talk to a neighbor for a little

while. Section C: He forgot his math book and goes back to

school. Section D: He walks directly home.

Yes; Possible explanation: The slope of the line at the

beginning of the graph is steeper than the slope of

the line at the end.

Possible explanation: The summary would describe the height

instead of the speed. The height starts at 0 and gradually

increases as the roller coaster goes up a hill. The height decreases

as the roller coaster goes down the hill and then increases as it

goes up a second hill. The height decreases again as the roller

coaster comes down the second hill and the height is 0 again.

M

41©

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Copyin

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itted.Practice an

d Problem

Solving

Unit 2 Fun

ctions Unit 2



Name: Lesson 10

Draw Qualitative Graphs

Study the example showing how to draw a qualitative graph. Then solve problems 1–8.

1 Why does the line in section A slant upward?

2 Why are the lines in sections B and D horizontal?

3 The price of a cable company’s service increases at a constant rate over time Would a sketch of the graph show the price starting at 0? Explain why or why not Then sketch a graph to show the price over time

4 Suppose the cable service price in problem 3 increases as stated and then stays constant for a limited time before increasing again Explain how the graph of this situation would diff er from the graph in problem 3

Example

To draw a qualitative graph for a story, you can break a story into parts and then draw a section for each part

Shane is riding his bike from home to the store and back

A From his house, he rides at a constant rate until he gets to the store

B He is at the store for a little while and

C starts to go back home On the way home,

D he stops at a friend’s house,

E then he rides the rest of the way home

The graph shows Shane’s distance from home compared to time

Time

Pric

eTime

Dis

tanc

e fr

om H

ome

A

B

C

D

E

107

B

B

Possible answer: It shows that Shane’s distance from home increases as the time increases.

They show that Shane stopped for a while, so his distance from home did not change.

No; Possible explanation: The price would never

have been $0.

M

Possible explanation: The line would increase for a while, then stay horizontal for a time, and

then increase again.

M


Solve.

5 Adele starts driving home from work On the way home, she stops at the grocery store Adele then drives home from the store at a slower rate than the fi rst part of her drive Sketch a graph that shows Adele’s distance from work compared to time

6 Jacob and Angel are riding bikes on a bike trail The fi rst part of the trail is steep, so they ride at a slow rate Halfway up, they stop and rest for several minutes Then they slowly continue up the steep part of the trail After reaching the highest part of the trail, they ride down at a constant rate that is faster than they rode up the fi rst part of the trail Sketch a graph to show the distance compared to time

7 Sales of computers at Tech Smart decrease at a constant rate for the fi rst few months of the year Then sales level off and stay the same for a couple of months Sales decrease again for a couple of months and fi nally increase gradually through the end of the year Sketch a graph to show the sales compared to time Explain your graph

8 Write a story for a qualitative graph Sketch a graph for your story, and then write a description for each segment of your graph

Time

Dis

tanc

e Ri

dden

Time

Sale

s

Time

Dis

tanc

e fr

om W

ork

108

M

M

M

C

Possible explanation: When the sales decrease

over time, the slope is negative. When the sales

stay the same, the line is horizontal. When the

sales increase, the slope is positive.

Stories and sketches will vary. Descriptions should

accurately explain the various segments shown in

the sketched graph. Sample description: Jenny’s

math scores increase as her study time increases.

M

Time

Mat

h S

core

s

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m A

ssociates, LL

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Copyin

g is not perm

itted.Practice an

d Problem

Solving

Unit 2 Fun

ctions

Unit 2



Name: Lesson 10

1 The graph represents Sophia’s distance from home

Time

Dis

tanc

e fr

om H

ome

Which one of these situations matches the graph?

A Sophia starts driving home, stops on the way to pick up a friend, and then continues driving home

B On the way home from work, Sophia makes two stops at different stores, staying in each store for a few minutes, and then drives home

C Sophia starts driving home, realizes that she forgot her cell phone at work, drives back to work for her phone, and then drives home

D Sophia walks to the bus stop, waits for the bus, then takes the bus home

Graphs of Functional Relationships

Solve the problems.

2 The battery life for Jacob’s laptop decreases as he uses it while unplugged until it fi nally dies It takes Jacob a while to fi nd a place to charge the battery When he fi nally plugs it in, the battery charges and gains more battery life Sketch a graph to represent the situation

Make sure that you think about the details in each description and where the graph starts: home or work.

When will the graph be increasing or decreasing? When will it be neither?

Time

Batt

ery

Life

109

B

M


Solve.

3 Mica takes a train to visit a friend The graph shows Mica’s trip from his home in New Jersey to his friend’s house in Maine

Which part of the graph shows Mica’s wait at the train station in New Jersey?

A I

B II

C IV

D V

Shakira chose C as the correct answer How did she get that answer?

4 This graph shows the temperature for a day in a city Tell whether each statement is True or False

Time

Tem

pera

ture

III

III

IV

a. Section I: The temperature increases for a few hours u True u False

b. Section II: The temperature decreases for few hours u True u False

c. Section III: The temperature stays the same for a few hours u True u False

d. Section IV: The temperature decreases from the high for the day until the end of the day u True u False

Compare each description to its corresponding section of the graph.

In which state did Mica start his trip?

Time

Dis

tanc

e fr

om H

ome

I II

III

IVV

110

M

Possible answer: Shakira chose the part that shows

Mica’s wait time at the train station in Maine.

3

3

3

3

M

lesson 10 - drauden point middle schooldpms.psd202.org/documents/ppotock1/1509025881.pdfpractice...

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