UNIT 2 - 1.cdn.edl.io fileUNIT 2 • LINEAR AND EXPONENTIAL RELATIONSHIPS Lesson 1: Graphs As...

UNIT 2 • LINEAR AND EXPONENTIAL RELATIONSHIPSLesson 1: Graphs As Solution Sets and Function Notation

Assessment

U2-71UCSS Secondary Mathematics I Teacher Resource

2.1© Walch Education

Name: Date:

Progress AssessmentCircle the letter of the best answer.

1. What is true about the set of all solutions for y = f(x)?

a. It can be graphed.

b. It is infinite.

c. It is a set of ordered pairs.

d. all of the above

2. The graphical representation of the solution set for y = f(x) is ______.

a. always a line

b. called a curve

c. a plane

d. a circle

3. Which of the following is true at the intersection of y = f(x) and y = g(x)?

a. f(x) = g(x)

b. x = 0

c. f(x) = 0

d. g(x) < f(x)

4. Which of the following does a sign change in the f(x) – g(x) column of a table of values imply?

a. y = f(x) has crossed y = g(x).

b. y = f(x) will not cross y = g(x).

c. y = f(x) equals y = g(x).

d. y = f(x) touched a point but did not cross y = g(x).

continued

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Unit 2A Study Guide


Assessment

U2-72UCSS Secondary Mathematics I Teacher Resource 2.1

© Walch Education

Name: Date:

5. What is the apparent range of the function graphed below?

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a. all real numbers

b. x < 6

c. f(x) > 0

d. infinity

6. If f(x) = 2x + 1 and the domain of f is {5, 25, 50}, what is the range of f(x)?

a. {5, 25, 50}

b. {10, 50, 100}

c. {11, 51, 101}

d. {0, 5, 10}

continued

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Assessment



Name: Date:

7. Given the graph below, what is f(6)?

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a. f(6) = 5

b. f(6) = 8

c. f(6) = –4

d. f(6) = 0

continued

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Assessment


© Walch Education

Name: Date:

8. Given the graph below, what is f(4)?

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a. f(4) = 3

b. f(4) = 5

c. f(4) = 2.25

d. f(4) = 8

9. DeAndre modeled the growth of his ant population using the function a xx

( ) 2(4) 3= , where x is in days. He started with 2 ants, and the population quadruples every 3 days. He evaluated the function at f(12) and calculated f(12) = 512. What does his calculation say about the ant population?

a. After 4 days, DeAndre will have 512 ants.

b. After 12 days, DeAndre will have 512 ants.

c. After 512 days, DeAndre will have 12 ants.

d. After 512 days, DeAndre will have about 171 ants.

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Assessment



Name: Date:

10. The contents of the fuel tank of a car can be modeled by the function g(x) = –0.04x + 15, where x is in miles driven and g(x) represents the amount of fuel remaining in the tank in gallons. Sierra has traveled 200 miles. Which statement represents the amount of gas in gallons that she has left in her car?

a. g(200) = 7

b. g(200) = 8

c. g(x) = 7

d. g(x) = 8

Read the scenario and use the information to complete the problem that follows.

11. Luisa is saving money to buy a new smartphone that costs $430. She started with $150 and every month she saves $20. Her savings can be modeled by the function s(x) = 20x + 150.

a. What are the domain and range of the function?

b. Evaluate the function after 4, 8, and 12 months of saving.

c. Interpret part b using a graph.

d. Write a statement using function notation that shows when Luisa will reach her goal. Then use words to describe the symbolic statement.

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UNIT 2 • LINEAR AND EXPONENTIAL RELATIONSHIPSLesson 2: Interpreting Graphs of Functions

Assessment


© Walch Education

Name: Date:


1. The graph below can be described as:

0 20 40 60 80 100 120 140 160 180 200 220 240

1

2

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4

5

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11

12

Miles

Am

ount

of g

as re

mai

ning

(gal

lons

)

a. having no maximum

b. having no minimum

c. having a maximum of 12 and a minimum of 0

d. having a maximum of 240 and a minimum of 0

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2. The graph below can be described as:

0 2 4 6 8 10 12 14 16 18 20 22 24

200

400

600

800

1000

1200

1400

1600

1800

2000

2200

Months

Am

ount

of m

oney

(dol

lars

)

a. a positive function that is increasing

b. a positive function that is decreasing

c. a negative function that is increasing

d. a negative function that is decreasing

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© Walch Education

Name: Date:

3. Which of the following graphs best represents the number of miles biked after a period of time?

a.

0 10 20 30 40 50 60 70 80 90 100 110 120

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Time (minutes)

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iles)

b.

0 10 20 30 40 50 60 70 80 90 100 110 120

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Time (minutes)

Dis

tanc

e (m

iles)

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Name: Date:

c.

0 10 20 30 40 50 60 70 80 90 100 110 120

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Time (minutes)

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Time (minutes)

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iles)

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Assessment


© Walch Education

Name: Date:

4. Use the table below to determine the rate of change for the interval [10, 15].

Weeks (x) Amount owed in dollars (f(x))0 15005 1350

10 120015 105020 900

a. $150 per week

b. $10 per week

c. $30 per week

d. $15 per week

5. Use the table below to determine the rate of change for the interval [2, 4].

Weeks (x) Value of stock in dollars (f(x))0 610.001 578.702 549.003 520.834 494.10

a. –$0.04 per week

b. –$27.45 per week

c. $27.45 per week

d. The rate of change cannot be determined.

6. What is the rate of change for the function f xx

=( ) 10(2) 2 over the interval [4, 8]?

a. 15

b. 30

c. 4


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Assessment



Name: Date:

7. What is the rate of change for the function f(x) = –3.2x + 5 over the interval [10, 20]?

a. –3.2

b. –32

c. –0.3125


8. The graph below represents the cost to rent mini-bikes over a period of time. What is the approximate rate of change for the function for the interval [0.5, 2.5]?

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6

15

30

45

60

75

90

105

120

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150

165

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225

240

255

Hours

Rent

al c

ost (

$)

a. $72.50 per hour

b. $0.03 per hour

c. $36.25 per hour

d. The rate of change cannot be determined.continued

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Unit 2A Study Guide


Assessment


© Walch Education

Name: Date:

9. The graph below represents the amount of an element in grams that remains after a period of time. What is the approximate rate of change for the function for the interval [0, 2.5]?

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

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80

100

120

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160

180

200

220

240

260

280

300

Minutes

Gra

ms

a. 116 grams per minute

b. –116 grams per minute

c. 290 grams per minute


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Name: Date:

10. The graph below represents the population of a small town over a period of time. What is the approximate rate of change for the function for the interval [6, 12]?

0 2 4 6 8 10 12 14 16 18 20

1000

2000

3000

4000

5000

6000

7000

8000

Years

Popu

lati

on

a. 500 people per year

b. –500 people per year

c. –3,000 people per year


continued

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Assessment


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Name: Date:

Use what you have learned about key features and rates of change to complete problem 11.

11. When a plant is introduced to a new outdoor environment, it can be difficult to tell whether the plant will adapt to the new conditions. Sometimes the plant will adapt too well and begin to overtake other nearby plants. When this happens, the rate at which the plant reproduces appears to explode. The graph below shows the population of a particular plant after it was introduced to a new environment.

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21

250

500

750

1000

1250

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1750

2000

2250

2500

Days

Plan

ts

a. What are the key features of this function and what do they mean in terms of this scenario? Be sure to include the intercepts, whether the function is increasing or decreasing, and whether the function is positive or negative; also, include any relative minimums and maximums as well as any asymptotes.

b. What is the domain of this function?

c. How does the rate of change vary over time?

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UNIT 2 • LINEAR AND EXPONENTIAL RELATIONSHIPSLesson 3: Analyzing Linear and Exponential Functions

Assessment


© Walch Education

Name: Date:


1. What is the y-intercept of the graph below?

a. (0, 1)

b. (–1, 0)

c. (0, –1)

d. (1, 0)

2. What is the x-intercept of the graph below?

a. (–5, 0)

b. (5, 0)

c. (0, –5)

d. (0, 5) continued

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Assessment



Name: Date:

3. What are the intercepts of the graph of f x x( )1

44= − ?

a. (0, 4) and (16, 0)

b. (0, 4) and (–16, 0)

c. (0, –4) and (–16, 0)

d. (0, –4) and (16, 0)

4. What is the best description of the end behavior of the graph below?

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a. growth, with a horizontal asymptote of y = 1

b. decay, with a horizontal asymptote of y = 0

c. growth, with a horizontal asymptote of y = 0

d. decay, with a horizontal asymptote of y = 1

5. What is the y-intercept of the graph of yx

31

52=

− ?

a. (0, –2)

b. (–2, 0)

c. (0, 1)

d. (1, 0) continued

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© Walch Education

Name: Date:

6. What is the y-intercept of the graph of f x x( )1

4(4) 2= + ?

a. (2, 0)

b. (2.25, 0)

c. (0, 2)

d. (0, 2.25)

7. What is the best description of the end behavior of the graph of f x x( )1

2(3 )= ?

a. growth, with a horizontal asymptote of y = 1

b. decay, with a horizontal asymptote of y = 3

c. growth, with a horizontal asymptote of y = 0

d. decay, with a horizontal asymptote of y = 0

8. Which inequality represents the graph?

Circle the letter of the correct answer to each question below.

1. Which inequality represents the graph below?

a. y ≤ x – 3

b. y ≤ x + 3

c. y > –x + 3

d. y ≥ x + 3


a. y < –x – 1

b. y > x – 1

c. y ≤ –x – 1

d. y ≤ x + 2

DAY 12 • MULTIPLE CHOICE PRACTICEGraphing Linear Inequalities on the Coordinate Plane and Systems of Inequalities

Georgiaacademic support program

NAME:

Georgia Academic Support Program: Mathematics, Grade 8 © 2009 Walch Education

482

y

x-5 -4 -3 -2 -1 1 2 3 4 5

543210

-1-2-3-4-5

y

x-5 -4 -3 -2 -1 1 2 3 4 5

543210

-1-2-3-4-5

continued

a. y < –x – 1

b. y > x – 1

c. y ≤ –x – 1

d. y ≤ x + 2

9. Which inequality represents the graph?

© 2009 Walch Education Georgia Academic Support Program: Mathematics, Grade 8

483


a. –3x + 2y ≤ 4

b. 3x + 2y ≥ –4

c. –3x – 2y ≥ –4

d. 3x – 2y ≤ 4

4. Which point is a solution to the inequality below?

y > x – 7

a. (3, –3)

b. (–3, –2)

c. (6, –4)

d. (–3, –15)

5. Which point is NOT a solution to the inequality below?

3x + 2y < 12

a. (–1, 1)

b. (0, 0)

c. (6, –3)

d. (2, –5)

DAY 12 • MULTIPLE CHOICE PRACTICEGraphing Linear Inequalities on the Coordinate Plane and Systems of Inequalities

Georgiaacademic support program

NAME:

y

x-5 -4 -3 -2 -1 1 2 3 4 5

543210

-1-2-3-4-5

4

3

continued

a. –3x + 2y ≤ 4

b. 3x + 2y ≥ –4

c. –3x – 2y ≥ –4

d. 3x – 2y ≤ 4

continued

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Assessment



Name: Date:

10. Which graph represents the solution to the inequality 4x + 3y ≥ 36?

a.

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b.

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c.

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d.

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Read the scenario and answer the question that follows.

11. A certain radioactive isotope has a half-life of 250 years. A scientist determines that there are 575 grams of the radioactive material present today. How much of the isotope was present 1,000 years ago?

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