Algebra 1 Q2 Packet - Maui High School

Algebra1Quarter2• LinearFunctions• Functions

x4è“xtothefourthpower”means“4factorsofx”

34è“3tothefourthpower”means“4factorsof3”

=3·3·3·3

=81

SlopeofaLine:"#$%&'(%)(+)"#$%&'(%+

Iff(x)isalinearfunctionrepresentingthepopulationofatownonMaui,thenwecanusethedatainthetabletodeterminetheslope,m,ofthegraphoff(x):

x (year)

f(x) (population of the town)

2003 13,000

2008 19,000

𝑚 =𝑐ℎ𝑎𝑛𝑔𝑒𝑖𝑛𝑓(𝑥)

𝑐ℎ𝑎𝑛𝑔𝑒𝑖𝑛𝑥

𝑚 =19000 − 130002008 − 2003

𝑚 =6000

5

𝑚 = 1200

Thismeansthatthepopulationincreasedby1200peopleeachyear.

SolvingEquations:findthenumberthatwillmakethestatementtrue.

25x+800=1300

25x+800=1300–800–800

25x=500

25x=5002525

1x=20Therefore,x=20.Check:doesx=20maketheoriginal equationatruestatement?

25x+800=1300

25(20)+800500+800

1300ü

A Refresher: Operations with Positive and Negative Numbers

Addition/Subtraction Multiplication/Division If the 2 numbers have the same signs:

add

Example A: 31 + 10 = 41

Example B: – 9 + (– 4) = – 13

Example C: – 413 – 200 = ____ è You should see this as negative 413 and negative 200 – 413 – 200 = ____ è Since they have the same signs, we add them.

– 413 – 200 = – 613 Example D: 50 – (– 40) = ____ è – (– 40) = 40, therefore, you should think of this as

positive 50 and positive 40 50 – (– 40) = 50 + 40 = 90

the answer is positive

Example H: 7 � 9 = 63 Example I: – 7 � – 8 = 56 Example J: – 7 � – 7 = 49 Example K: 64 ÷ 8 = 8 Example L: – 72 ÷ – 8 = 9

If the 2 numbers have DIFFERENT signs:

SUBTRACT

Example E: 31 – 45 = ____ è 31 – 45 = ____

èThink about this as positive 31 and negative 45

è Since the numbers have DIFFERENT signs, we SUBTRACT.

è The sign of the larger quantity is also the sign of the answer.

31 – 45 = – 14

Example F: – 123 + 100 = ____ è – 123 + 100

è You should see this as negative 123 and positive 100; since they have DIFFERENT signs, we SUBTRACT.

è The sign of the larger quantity is also the sign of the answer. – 123 + 100 = – 23

Example G: – 12 – (– 19) = ____ è – 12 – (– 19)

è – (– 19) = 19, therefore, we should think of this problem as negative 12 and positive 19 – 12 + 19 = 7

è since they have DIFFERENT signs, we SUBTRACT. è The sign of the larger quantity is also the sign of the

answer.

The answer is NEGATIVE

Example M: – 6 � 9 = – 54 Example N: 6 � – 8 = – 48 Example O: – 42 ÷ 6 = – 7 Example P: 36 ÷ – 6 = – 6

Algebra 1 Quarter 2 Table of Contents

Lesson Title Page M

odul

e 3:

L

inea

r Fu

nctio

ns

L-6.1 Introduction to Scatter Plots 1 L-6.2 Homework (Graphing Review) 7 L-6.3 Line of Best Fit and Linear Regression 9 L-6.4 Homework 15 L-7.1 Linear Models – Pole Vaulting Investigation 17 L-7.2 Homework 21 L-8.1 Warm-up (Inequalities) 23 L-8.2 Solving Equations & Inequalities Graphically 25 L-8.3 Solving Inequalities 29 L-8.4 Linear Inequalities in Context 33 L-6 through L8 Review 37

Mod

ule

4: F

unct

ions

F-5.1 Matching Stories with their Graphs 39 F-5.2 Interpreting Graphs in Context 43 F-5.3 Interpreting Graphs in Context (continued) 47 F-5.4 Homework 51 F-5.5 Stations Activity 55 F-5.6 Interpreting Graphs in Context (continued) 57 F-6.1 Interpreting the Shape of a Graph 63 F-6.2 Interpreting Graphs Showing Change Over Time 71 F-6.3 Graphing Stories 75 F-6.4 Graphing Scenarios with more Precision 79 F-6.5 Homework 83 F-6.6 Distance, Rate and Time 85 F-7.1 Linear Functions Revisited 91 F-7.2 Homework 97 F-7.3 Absolute Value 99 F-7.4 Solving Equations Graphically 103 F-7.5 Homework 107 F-7.6 Solving Quadratic Equations Graphically 109 F-7.7 Homework 113 F-7.8 Stations Activity 115 F-7.9 Homework 117 F-8.1 Inequalities in Context 119 F-8.2 Solving Inequalities Graphically 121 F-8.3 Stations Activity 125

Appendix Vocabulary Section 129

Algebra 1 – Module 3: Linear Functions Name _______________________________ L-6.1: Introduction to Scatter Plots Pd ____________ Date _______________

© 2016 Hawaii Department of Education Licensed under the Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported license. 1

Part I: Warm-up (follow your teacher’s instructions) 1.

2. To improve his fitness for the upcoming basketball season, Mike started a new nutrition and

exercise program. The table shows his weight at the end of each week after he started the program.

5 10 15 20 25 30 35 40 45 50

50

45

40

35

30

25

20

15

10

5

Week Number

Weight at the end of the week

1 200 2 195 3 193 4 190 5 185 6 182 7 180 8 176



Part II: Recognizing and Describing Trends in Data

Plot the data set in the coordinate plane provided and answer the questions that follow. Before plotting any points,

• provide a title for what the x-axis and y-axis represent;

• choose an appropriate scale for the units on each axis and label each axis accordingly;

• decide if you should use a “scale break” on each axis. 3. Lexi tracks how much time she studies for tests and records the resulting percentage she earns on

subsequent tests in the table below.

b. Circle one of the underlined options that best describes the relationship between study time and test

score:

As Lexi’s study time increases, her test scores increase / decrease / have no linear relationship.

c. Based on your scatter plot, what would her approximate test score be if Lexi studied for 20 minutes? Explain how you got your answer.

d. Based on the trend, estimate how long Lexi needs to study in order to earn 80%. Explain how you

got your answer

Study Time (Min)

Test Score (%)

60 92 55 72 10 65 75 87 120 98 90 95 15 68

y

x

a. Lexi analyzed her graph and said, “This scatter plot seems to have a linear trend.” Explain why you think Lexi would make that conclusion.



4. Following your teacher’s instructions, use the situation below to explore how to use a scatter plot to

represent and analyze bivariate data. Students in a Physics class were studying the relationship between how high a tennis ball will

bounce after being dropped from various heights. Taylor and Carly worked as partners to collect the data shown in the table below.

Labe

l for

y-a

xis:

__

____

____

____

____

____

____

label for x-axis: __________________________________

Height that the ball was dropped from

(centimeters)

Height of the first bounce

(centimeters) 150 80 120 65 100 57 80 45 60 35 50 30 40 23 30 15



5. In 1912, the people of Japan sent 3,020 cherry trees to the United States as a gift of friendship. The date the trees reach full blossom (approximately 70% in bloom) varies each year depending on the weather. The table below shows various dates in April when the famous Washington, DC, cherry trees bloomed and the average winter temperature that year.

Labe

l for

y-a

xis:

___

____

____

____

____

____

label for x-axis: __________________________________

Year Day of the Year

Avg. Winter Temp in Wash. DC (˚F)

1993 101 38.5 1994 95 41.1 1995 92 42.1 1996 95 40.2 1997 85 46.8 1998 86 45.2 1999 95 42.8 2000 77 47.2 2001 96 42.4 2002 92 45.3 2003 92 44.7 2004 91 43.0 2005 99 41.4 2006 89 43.5 2007 91 39.8 2008 86 45.2 2009 91 42.0 2010 90 43.2 2011 88 43.8

Plot the data set in the coordinate plane provided and answer the questions that follow. Before plotting any points,

• provide a title for what the x-axis and y-axis represent;

• choose an appropriate scale for the units on each axis and label each axis accordingly;

• decide if you should use a “scale break” on each axis.



Use your scatter plot on the previous page to answer the following questions. a. Does the scatter plot look to be approximately linear to you? Explain why or why not.

b. Describe the relationship between the day of the year the cherry blossoms bloom and the average

winter temperature in Washington, DC, by circling one of the underlined choices: “As the day of the year increases, the average winter temperature in Washington

Increases / decreases / has no linear relationship.” c. Based on your scatter plot, approximately what would be the average winter temperature if the

bloom happened 87 days into the year? Explain how you arrived at your answer.

d. Based on your scatter plot, approximately what day of the year would the cheery trees bloom if the average winter temperature that year was 35 degrees? Explain how you arrived at your answer.



6. The table below shows the relationship between the month of the year and the amount of rainfall in

Algarve, Portugal, from the years 1970 – 1995. Create a scatter plot of the data and answer the questions that follow.

a. Does the scatter plot look to be linear to you? Explain.

b. Describe the relationship between the month number as the average rainfall by circling one of the following: “As the month number increases, the average rainfall

Increases / decreases / has no linear relationship.”

c. Based on your plotted points, can you predict the approximate month of the year when there was 30.8 mm of rain? Why or why not?

Part III: Reflect and summarize (follow your teacher’s instructions).

Month Number

Average Rainfall (mm)

1 69.9 2 58.0 3 32.7 4 42.1 5 21.0 6 8.1 7 1.0 8 2.0 9 12.1

10 59.6 11 79.3 12 96.3

Algebra 1 – Module 3: Linear Functions Name _______________________________ L-6.2: Homework (Graphing Review) Pd ____________ Date _______________


1. Determine the symbolic representation for each graph shown below. Express your answer in slope-

intercept form: f(x) = mx + b. A. _______________________________ B. _______________________________

C. _______________________________ D. _______________________________

Algebra 1 – Module 3: Linear Functions Name _______________________________ L-6.2: Homework (Graphing Review) Pd ____________ Date _______________


2. Graph the following functions in the coordinate plane below. Label each graph with its function

name.

f(x) = -4x + 1 g(x) = -3 – 2x h(x) = x – 6 𝑘 𝑥 = $%𝑥 + 7

3. Use the functions stated above (in question #2) to determine the value of the function at x = 15.

Show how you determined your answer. A. f(15) B. k(15)

4. Use the functions stated above (in question #2) to determine for what value of x the function will have a value of 60. Show how you determined your answer.

A. h(x) = 60 B. g(x) = 60

Algebra 1 – Module 3: Linear Functions Name _______________________________ L-6.3: Line of Best Fit and Linear Regression Pd ____________ Date _______________


Part I: Warm-up (follow your teacher’s instructions)



Part II: Line of best fit When a scatter plot appears to have a linear trend, we want to determine the graph of a line that gets as “close to” as many of the data points as possible and seems to best represent the linear relationship. This is called the line of best fit. 1. All 4 scatter plots below show the same data set, but with a different line drawn through the set of

points. Circle the graph that appears to show the most accurate line of best fit for the data set.

2. With a partner list a few characteristics that you should look for when identifying a line of best fit

for a data set.



3. Consider the scatter plot below. a. Draw the line of best fit for the data set that is represented in the graph.

b. Select two points that lie on the line of best fit that you drew (these do not need to be data points!).

Write your two points below. c. Use these two points to determine the symbolic representation of your line of best fit. Express your

answer in slope-intercept form: f(x) = mx + b.



Part III: Linear regression

For each situation that follows, use the given data set to determine the line of best fit that represents the trend in the data. Then, use your line of best fit to answer the questions regarding the given situation. 4. The table shows Tammy’s speed at typing after a given number of weeks practicing. Create a scatter

plot of the data.

a. Draw the line of best fit and determine its symbolic representation. b. Using the function you created above (for your line of best fit), describe what each of your variables

represents. c. In your function, what does the slope mean in the context of the given situation? What does the y-

intercept mean in the context of the given situation?

d. Use your line of best fit to predict how many words per minute Tammy will type after 12 weeks of practice.

e. Use your line of best fit to predict how many weeks of practice it will it take for Tammy to type 100 words per minute.

Practice time (weeks)

Typing Speed (words per

minute) 1 20 2 22 3 30 4 33 5 38 6 40 7 44



5. The geyser Old Faithful can be found in Yellowstone National Park. For more than 100 years, Old

Faithful has erupted every day, several times each day. Create a scatter plot of the data provided.




d. Use your function (for your line of best fit) to predict when the next eruption will be if the length of the last eruption was 2.3 minutes.

e. Use your line of best fit to predict the length of an eruption if the time until the next eruption is 70 minutes.

Length of Eruption (minutes)

Time until next eruption

(minutes) 2 57

2.5 62 3 68

3.5 75 4 83

4.5 89 5 92



6. The table below shows the hours of TV watched weekly by 9 students and their scores on a math quiz. Plot the data points.




d. Use your function (for your line of best fit) to predict the quiz score of a student who watched 20 hours of TV.

e. Use your function to predict the number of hours of TV someone watched if he/she scored a 70 on the quiz.

TV (hours) Math Quiz Score (%)

21 70 8 100

31 44 15 72 21 54 28 40 10 20 18 96 17 64

Algebra 1 – Module 3: Linear Functions Name _______________________________ L-6.4: Homework Pd ____________ Date _______________


1. The table below shows the length and weight of several adult humpback whales. Create a scatter plot of the data set.



intercept mean in the context of the given situation? d. Use your function (for your line of best fit) to predict the weight of a 48-foot humpback whale.

e. Use your function to predict the length of a humpback whale that weighs 60 long tons.

Length(ft.) Weight(tons)

40 2542 2945 3446 3550 4352 4555 51



2. The table below represents the life expectancy of people born in Hawaii during given years. Plot the data points.



intercept mean in the context of the given situation? d. Use your function (for your line of best fit) to predict the life expectancy for someone born in

Hawaii in the year 2000.

e. At one point in time, the life expectancy for someone born in Hawaii was only 40 years. Use your function to predict when someone with a life expectancy of 40 years might have been born.

Year of Birth Life Expectancy (Years)

1910 43.9 1930 54.3 1950 69.75 1970 74.2 1990 79 1920 45.7 1940 62.4 1960 72.6 1980 78

Algebra 1 – Module 3: Linear Functions Name _______________________________ L-7.1: Linear Models – Pole Vaulting Investigation Pd ____________ Date _______________


Part I: Warm-up (follow your teacher’s instructions).



Part II: Problem solving and modeling with linear relationships Keanani comes from a long line of professional pole-vaulters. She wants to follow in her family’s footsteps and get a track scholarship to the University of Hawaii. She began practicing the pole vault for 180 days before her high school freshmen track season. She found out that for every 30 days she practices, she improves her pole vault height by approximately 1 inch. 1. How many inches did she improve over the first 60 days? 2. How many inches did she improve over the first 120 days? 3. How many inches did she improve over the 180 days? 4. How did you determine your answers for questions 1-3? 5. Using t for the number of training days, write an expression that represents the number of inches she

improves over t days of training. On the 180th day, she reached her first goal of pole-vaulting 12 ft. (144 inches). 6. How many inches could Keanani pole vault at the beginning of the 180 days? 7. How many inches could she pole vault after 90 days of training? 8. How many inches could she pole vault after 150 days of training? 9. How did you determine your answers to questions 6,7, and 8?



10. Using your expression from question 5, determine a symbolic representation for the height Keanani can pole vault, H(t), t days after she began training.

11. Graph the linear function H(t) function below. Be sure to label your axes.

12. What does the y-intercept represent in context? 13. What is the rate of change of this function and what does it represent in context? 14. What is another name for the rate of change of a linear function? 15. If Keanani continues practicing and continues to improve at the same rate, how high will she be able

to pole vault after 240 days?



16. How high can she pole vault after 195 days? 17. How long will it take her to reach 13 ft.? 18. How long will it take her to reach 13 ½ ft.? Part III:

After 1 year, a new coach was hired by the high school, and Keanani’s sister Alexis started practicing pole vaulting. The new coach showed Alexis a better way to practice. She could improve her height by 1 inch every 20 days. Alexis was able to start at the same height that Keanani started at. 19. Determine the symbolic representation for A(t). 20. Graph A(t) below. Be sure to label your axes.

21. If Keanani is stubborn and refuses to change her training techniques, at which point in time will

Alexis catch up with her and then pass her? How high will the girls be able to pole vault at that time?



Freddie decides he wants to lose some weight before his daughter gets married so he can fit into his suit. During the past year, he broke his leg and has not been able to exercise. Since he and his wife love to barbecue at Makaha Beach Park every weekend, he’s packed on a few pounds. Luckily, his doctor just found a new diet and exercise routine for him now that his leg is healed. After 30 days, he found out his weight is continuing to decrease linearly. On day 20, his weight was 220 lbs. On day 30, today, his weight was 215 lbs.

1. Explain how his weight is changing in terms of the number of days since he began the program.

2. How many pounds does his weight change per day?

3. Write an expression to express change in pounds per d days of exercise.

4. How much weight will he lose after 60 days on the program?

5. How much did he weigh when he began the program?

6. How much did he weigh after 10 days?

7. How much will he weigh after 50 days?

8. How much will he weigh after 66 days



9. Determine the function that represents Freddie’s weight, F(d), d days after he began the

program.

10. Is the slope of F(d) positive or negative? Explain why this makes sense in this context.

11. How long will it take him to reach his goal weight of 170 lbs.?

12. Will he reach this goal before his daughter gets married 4 months from today? Explain how you know.

13. Graph your function F(d) below. Be sure to label your axes.

Algebra 1 – Module 3: Linear Functions Name _______________________________ L-8.1: Warm-up (Inequalities) Pd ____________ Date _______________


Part I: Warm-up (follow your teacher’s instructions).

Symbol Meaning Key Words Example Representation on a Number Line

≠

>

≥

<

≤

Algebra 1 – Module 3: Linear Functions Name _______________________________ L-8.1: Warm-up (Inequalities) Pd ____________ Date _______________


Part II: Connecting different representations of inequality statements For each row, fill in the missing columns to show different ways of representing the same inequality. Then, in the last column, circle all values that are solutions to the inequality represented in that row.

Symbolic Notation

Verbal Description Set Notation Number Line Graph

Possible Solutions

(Circle all true)

x > 3 9 -2 1

2 6

−83

0 12 -3

All values x less than or equal to 2.

9 -2 12

6

−83

0 12 -3

{ x : x < }

9 -2 12

6

−83

0 12 -3

9 -2 12

6

−83

0 12 -3

All values x strictly greater than 2 and less than or equal to

than 6.

9 -2 1

2 6

−83

0 12 -3

x 9 -2 1

2 6

−83

0 12 -3

23

4£ -

Algebra 1 – Module 3: Linear Functions Name _______________________________ L-8.2: Solving Equations & Inequalities Graphically Pd ____________ Date _______________


Part I: Warm-up 1. Shade all boxes with x values 2. Shade all boxes with x values such that f(x) > 4. such that g(x) > 0.

x f(x) -5 -8 -4 -5 -3 -2 -2 1 -1 4 0 7 1 10 2 13 3 16

x g(x) -3 2.5 -2 2 -1 1.5 0 1 1 0.5 2 0 3 -0.5 4 -1 5 -1.5

3. The graph of f(x) is shown below. Note:

this is the same function whose table of values is provided in question 1.

a. Circle the portion of the graph that

shows all values such that f(x) > 4. b. Shade the section on the x-axis that

contains all x-values that correspond to the portion of the graph that you circled.

4. The graph of g(x) is shown below. Note: this is the same function whose table of values is provided in question 2.

a. Circle the portion of the graph that

shows all values such that g(x) > 0. b. Shade the section on the x-axis that

contains all x-values that correspond to the portion of the graph that you circled.

Thescaleusedoneachaxisis1unit.

f(x)

Thescaleusedoneachaxisis1unit.

g(x)



5. The functions used to create the table of values in questions 1 and 2 (on the previous page) are

𝑓 𝑥 = 3𝑥 + 7 and 𝑔 𝑥 = −12 𝑥 + 1

The graphs of f(x) and g(x) are now shown together in the same coordinate plane.

f(x)

g(x)

a. When x = 0, is f(x) > g(x)?

Explain how you can use the graphs above to support your conclusion.

b. Evaluate each function to verify that f(x) > g(x) when x = 0.

c. When x = -2, is f(x) > g(x)?

Explain how you can use the graphs above to support your conclusion.

d. Evaluate each function to verify that f(x) < g(x) when x = -2.



Part II: Comparing the values of 2 functions

Use the following graphs of linear functions to answer the accompanying questions. 1. 2.

a. Which is greater, f (2) or g(2)? How do you

know? b. For which value of x is f (x) = g (x)?

c. For which values of x is 𝑓 𝑥 ≥ 𝑔(𝑥)? Write

your answer in set notation.

d. For which values of x is f (x) < g (x)? Write

your answer in Set Notation.

a. Is f (-4) < g (-4)? Explain how you can tell.

b. For which values of x is it true that 𝑓 𝑥 ≤

𝑔 𝑥 ? Write your answer in set notation.

c. For which values of x is it true that 𝑓 𝑥 ≥

𝑔 𝑥 ? Show the solution on the number line below (label the units on the number line).



3.

a. When x = 1, is g(x) or f (x)greater? How do you know?

b. For which value of x is it true that f(x) = g(x)?

c. For which values of x is it true that g(x) > f(x)? • First, express the solution in set notation. • Then, show the solution on the number line below (label the units on the number line).

Algebra 1 – Module 3: Linear Functions Name _______________________________ L-8.3: Solving Inequalities Pd ____________ Date _______________


Part I: Warm-up Solve each equation. Show how you determined your solution. 1. 3 2x − 5( ) = 55− 4x 2. 13x − 2(4x − 7) = 9 3. 9x − 5− x + 2 = 4(1+ 2x) Part II: Solving inequalities algebraically Following your teacher’s instructions, use the space below to take notes regarding the functions graphed

in the coordinate plane: p(x) = 2x − 2 and r(x) =1− 4x

p r



Let’s explore the solutions to two other inequalities.

Example A: First, analyze graphs of K(x) and L(x): • Circle the portion of the graph where it appears that

K(x) ≤ L(x) . • Then, shade all of the values along the x-axis that

correspond to the portion of the graph that you circled.

Second, make a guess: • What do you think is the solution to K(x) ≤ L(x) ?

Now, let’s solve the inequality: K(x) ≤ L(x)

−x − 2 ≤ 3x + 2 Example B: First, analyze graphs of c(x) and h(x): • Circle the portion of the graph where it appears that

c(x)> h(x) . • Then, shade all of the values along the x-axis that

correspond to the portion of the graph that you circled.

Second, make a guess: • What do you think is the solution to the inequality

c(x)> h(x) ? Now, let’s solve the inequality: c(x) > h(x)

−3x + 1 > − x − 3

K(x) = -x – 2

L(x) = 3x + 2

The scale on each axis is 1 unit.

The scale on each axis is 1 unit.

c(x) = -3x + 1

h(x) = -x – 3



4. Solve each inequality. a. 3 x − 2( ) < 9 b. 10x − 1 ≥ 49 c. 2x − 3 ≤ 9 − 2x

d. 15

20 − 5x( ) > 12

(6x + 14) − 3x e. 12 ≤ 4 9 − 2x( )

5. Set up and solve an inequality using the given functions. Write your solution in set notation and

represent it on the number line provided (label the units on the number line).

a. Given 𝑓 𝑥 = 𝑥 − 3 and 𝑔 𝑥 = − 7%𝑥 + 2,

determine all values of x such that f(x) > g(x). Answer in set notation: __________________ Solution set represented on a number line:

b. Given 𝑓 𝑥 = −3𝑥 − 1 and 𝑔 𝑥 = − 87𝑥,

determine all values of x such that f(x) < g(x). Answer in set notation: _________________ Solution set represented on a number line:



c. Given 𝑓 𝑥 = − 7

%𝑥 − 2 and

𝑔 𝑥 = − $7𝑥 − 3, determine all values of x

such that 𝑓(x) ≤ g(x). Answer in set notation: __________________ Solution set represented on a number line:

d. Given 𝑓 𝑥 = −𝑥 + $7 and

𝑔 𝑥 = − $7𝑥 + 2, determine all values of x

such that 𝑓(x) ≥ g(x). Answer in set notation: _________________ Solution set represented on a number line:

Part III: Reflect and summarize (follow your teacher’s instructions)

Solving Multi-Step Equations and Inequalities

Similarities Differences

Algebra 1 – Module 3: Linear Functions Name _______________________________ L-8.4: Linear Inequalities in Context Pd ____________ Date _______________


Part I: Warm-up (follow your teacher’s instructions) Caitlyn notices that her compact sedan has very good fuel mileage around town; while Brent’s large truck does not. The car manual for both cars provides the following information:

• Caitlyns’s car starts at 40 miles per gallon (mpg) but decreases by 2 mpg with every increase of 5 miles per hour (mph) in speed.

• Brent’s truck starts at 10 mpg, but increases by 3 mpg with every increase of 8 mph.

At what speed will Brent’s truck get better fuel mileage than Caitlyn’s car?

Fuel

Mile

age

Rat

e (m

pg)

70

60

50

40

30

20

10

10 20 30 40 50 60 70 80

The Speed the Vehicle is Traveling at (mph)



Part II: Solving linear inequalities in real-world situations 1. Sharon needs to move tomorrow for her new job. She rents a U-Haul truck to move her belongings.

It costs $30 to rent the truck she needs, plus $0.50 per mile to rent the truck she needs. Let P(m) be the price of renting the truck and driving it for m miles.

a. Write the symbolic representation of P(m):

b. Sharon has budgeted $200 for the truck rental. How many miles can she drive on her budget? To find the answer, solve for m such that 𝑃(𝑚) ≤ 200. Represent your answer in Set Notation.

c. Sharon wanted to save money, so she went online to find alternate truck rental companies. She found that Freddy’s garage can rent her a truck for a flat rate of $100. So, she wants to compare under what conditions it will be cheaper for her to rent from U-Haul versus Freddy’s garage. Solve for m such that P(m) < 100 to find the answer. Represent your answer in set notation.

d. Sharon computes the distance she will need to drive during the move. She determines that she will drive 120 miles. Should she rent from U-Haul or from Freddy’s garage? Explain your answer.

2. When mobile (cell) phones became popular (around the year 2000), people had to purchase a “text

messaging plan.” Back then, a company offered 2 text messaging plans that customers could choose:

• Plan A charges a monthly fee of $5.00 plus $.10 per text.

• Plan B charges a monthly fee of $10.00 plus $.05 per text.

a. Let A(t) be the cost of plan A if t texts are used. Write the symbolic representation of A(t).

b. Let B(t) be the cost of plan B if t texts are used. Write the symbolic representation of B(t).

c. In the context of the given situation, explain what the inequality A(t) < B(t) is really asking.



d. Set up and solve the inequality A(t) < B(t) using the functions you created above in 2a and 2b.

e. Explain what your solution above (in 2d) means in the context of the given situation.

f. If a customer estimated they would send about 200 texts per month. Which plan (A or B) should she choose? Explain why you decided that plan would be best.

g. In the context of the given situation, explain what the inequality A(t) < B(t) is really asking.

h. Kyla’s parents said they would pay at most $20 per month for her texting plan. If her parents selected plan A, how many texts can she send without going past the $20 limit? Set up and solve an inequality using the function you created for plan A.



Set-up and solve an inequality to answer the questions in each scenario below. 3. A new company offers customers the opportunity to watch TV shows on their computer (or tablet, or

smart phone). The company has two plans that customers can choose from:

• Plan A: Join as a Premier Member, where you pay a monthly $14 membership fee plus $2 for each TV show you watch.

• Plan B: Join as a Regular Member, which has no membership fee, but charges $5 for each TV show you watch.

Determine how many TV shows you need to watch in order for the Premier Membership to be the

better bargain. 4. Dustin wants to start taking yoga classes. He does some research and is trying to decide between two

yoga studios.

• Laulea Yoga studio charges a monthly membership fee of $30 plus $3 per class that you attend.

• Waipahu Yoga School charges a monthly membership fee of $12 plus $5 per class that you attend.

Make a recommendation to Dustin regarding which yoga studio would be cheaper. Justify your

answer.

Algebra 1 – Module 3: Linear Functions Name _______________________________ L-6 through L8 Review Pd ____________ Date _______________


Follow your teacher’s instructions.

Algebra 1 – Module 3: Linear Functions Name _______________________________ L-6 through L8 Review Pd ____________ Date _______________


Algebra 1 – Module 4: Functions Name _______________________________ F-5.1: Matching Stories with their Graphs Pd ____________ Date _______________


Part I: Warm-up (follow your teacher’s instructions) A

Dis

tanc

e fr

om h

ome

Time

B

Dis

tanc

e fr

om h

ome

Time

C

Dis

tanc

e fr

om h

ome

Time

D

Dis

tanc

e fr

om h

ome

Time



Part II: Matching a story with its graph (follow your teacher’s instructions)

1 Keahi started walking slowly to work knowing he had given himself plenty of time to get there. But after stopping to talk to a friend along the way, he realized he was late and ran to make it to work on time.

2 Not wanting to be late for school, Keahi left his house running in an attempt to make it to his bus stop on time. After waiting for a few minutes at the bus stop, he realized it was Saturday and walked back home.

3 Keahi went out to climb the hill behind his house. He climbed slowly up the hill, walked quickly across the top, and ran joyfully down the other side.

4 After spending the day at the beach, Keahi walked slowly back to his house at the same rate the whole way.

5 Keahi set out to walk his dog to the park. Halfway to the park he realized he had left his dog at home. After going back home to get his dog, they ran to the park together.

6 Keahi walked to his friend’s house, hung out awhile, and then ran home just in time for dinner.

7 Keahi set out walking to meet a friend at the movies. When he got about halfway there, he realized that he left his wallet at home and started heading back. But then he found $20 in his pocket, decided he could do without his wallet, and walked quickly to get to the movie on time.

8 This graph makes no sense. How can Keahi possibly move farther from home without any time elapsing?



Distance v. Time Graphs A

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tanc

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Time

B

Dis

tanc

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Time

C

Dis

tanc

e fr

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ome

Time

D

Dis

tanc

e fr

om h

ome

Time

E

Dis

tanc

e fr

om h

ome

Time

F

Dis

tanc

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ome

Time

G

Dis

tanc

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Time

H

Dis

tanc

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Time


This page is intentionally left blank (If you choose to, you may use this page for notes or to create your own

“distance vs. time” graphs/stories).

Algebra 1 – Module 4: Functions Name _______________________________ F-5.2: Interpreting Graphs in Context Pd ____________ Date _______________


Part I: Interpreting graphs in context

Answer the questions pertaining to each graph.

1. The following graph shows Mehana’s distance from home on her Sunday afternoon travels as she sets out walking at noon to meet a friend.

D

ista

nce

from

hom

e (m

i)

4 3 2 1 0

1 2 3 4

Time (hours) a. Where was Mehana at noon? b. Approximately when was Mehana farthest from home? c. What is the farthest Mehana traveled from home?

d. How far from home was Mehana at 2:30pm? e. Approximately when was Mehana 1 mile from home?

f. When did Mehana return home? g. Describe what Mehana might be doing between 1:00 and 1:30pm.



2. The following graph shows Logan’s height above the ground in feet as he climbs a tree to get a

coconut.

H

eigh

t (ft.

)

48 36 24 12 0

4 8 12 16

Time (min) a. Where was Logan when no time had elapsed? b. How high did Logan climb? c. When did Logan reach his maximum height? d. How many feet above the ground was Logan after 12 minutes? e. When was Logan 24 feet above the ground? f. When 18 minutes had passed, where was Logan? g. Describe what Logan might be doing between 4 and 6 minutes.



3. The following graph shows Taylor’s speed in miles/hour while driving to the store.

S

peed

(mph

)

40 30 20 10 0

2 4 6 8

Time (min) a. When did Taylor reach her maximum speed? b. What was Taylor’s maximum speed? c. How fast was Taylor driving 5 minutes into her trip? d. When was Taylor traveling at 10 mph? e. When did Taylor stop? f. Describe what Taylor might be doing between 2 and 3 minutes.



Part II: Reflect and Summarize (follow your teacher’s instructions). Reflection #1:

a. In Graph #1, the highest point (2, 3.5) tells us that Mehana has reached her maximum

__________________________________. In other words, it took Mehana _________ hours to

walk _________ miles from home.

b. In Graph #2, the highest point (8, 42) tells us that Logan has reached his maximum

__________________________________. In other words, it took Logan _________ minutes to

climb to a height of _________ feet above the ground.

c. In Graph #3, the highest point (4, 35) tells us that Taylor has reached her maximum

_________________________________. In other words, it took Taylor _________ minutes to

reach a speed of _________ miles per hour.

Reflection #2: The x-intercepts on each graph have a different meaning due to the label on the y-axis.

a. In Graph #1, the x-intercepts tell us the times at which Mehana is _________________________. b. In Graph #2, the x-intercepts tell us the times at which Logan is _________________________. c. In Graph #3, the x-intercepts tell us the times at which Taylor is _________________________.

Reflection #3: The flat/horizontal sections on each graph also have a different meaning due to the label on the y-axis.

a. In Graph #1, the horizontal section tells us that Mehana is _____________________________. b. In Graph #2, the horizontal section tells us that Logan is _____________________________. c. In Graph #3, the horizontal section tells us that Taylor is _____________________________.

Algebra 1 – Module 4: Functions Name _______________________________ F-5.3: Interpreting Graphs in Context (continued) Pd ____________ Date _______________


Part I: Interpreting graphs in context

Answer the questions pertaining to each graph.

1. Jenny sets out at 7:00 a.m. to go for a jog. The following graph shows her distance D(t) from home, in miles, as a function of time t, in minutes, starting at 7:00 a.m.

D(t)

D

ista

nce

from

hom

e (m

i) 4 3 2 1 0

t 20 40 60 80

Time (min) a. Where was Jenny at 7:00 a.m.? b. Approximately when was Jenny farthest from home? c. What is the farthest Jenny traveled from home? d. How far from home was Jenny at 8:00 a.m.? e. For what value(s) of t does D(t) = 3? Explain the meaning of your answer(s) in context. f. At what time did Jenny return home? g. Describe what Jenny might be doing between 7:10 a.m. and 7:20 a.m.



2. The following graph shows the temperature T(t), in degrees Celsius, at a certain crater on the planet

Mercury, t minutes after sunrise.

Tem

pera

ture

80 40 0 -40 -80

1 2 3 4 5 6 7 8 Time since sunrise (min)

a. What was the temperature at sunrise? b. What is the value for T(8) and what does it represent in context? c. When was the temperature 30 degrees below 0? d. When did the temperature reach 0 degrees Celsius? Explain how you know. e. How long did it take after sunrise for the temperature to reach 30 degrees above 0?



3. Kaleo leans over and throws a ball straight upward from a rooftop. The following graph shows the

height h(t) of the ball, in feet, over time t, in seconds beginning at the moment he released the ball. h(t)

Hei

ght (

ft.)

80 60 40 20 0

t 1 2 3 4

Time (sec) a. What is the value of h(0)? What does your answer mean in context? b. When did the ball reach its maximum height? c. What was the maximum height of the ball? d. For what value(s) of t does h(t) = 0? Explain the meaning of your answer(s) in context. e. Did the ball land back on the roof? Explain how you know. f. Approximately when was the ball 80 feet above the ground?



Part II: Follow your teacher’s instructions. 1. Title: ___________________________________________

Lab

el fo

r y-

axis

: __

____

____

____

____

____

____

_

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Time (seconds)

2. Title: ___________________________________________

Lab

el fo

r y-

axis

: __

____

____

____

____

____

____

_

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Time (seconds)

Algebra 1 – Module 4: Functions Name _______________________________ F-5.4: Homework Pd ____________ Date _______________


1. The graph below shows Jessica’s projected SAT math score as a function of the number of practice

tests she takes.

Pr

ojec

ted

Scor

e

800 600 400 200 0

2 4 6 8 # of Practice Tests

a. What is Jessica’s projected SAT math score if she doesn’t take any practice tests? b. What is Jessica’s projected SAT math score if she takes 7 practice tests? c. How much could Jessica improve her score by taking 2 practice tests? d. What is the minimum number of practice tests Jessica must take if her goal is to earn a score of at

least 550? e. How many practice tests should Jessica take to maximize her score? f. What is Jessica’s maximum projected score?



2. Malia plans to order some t-shirts for a fundraiser. The following graph shows the cost per shirt as

a function of the number of shirts ordered.

C

ost p

er sh

irt

24 18 12 6 0

50 100 150 200 # of t-shirts ordered

a. Approximately how much will Malia pay if she only orders one t-shirt? b. What is the cost per shirt if Malia decides to order 100 t-shirts? c. How many shirts does Malia need to order for each shirt to cost $18? d. Malia plans to sell the shirts for $15 and would like to earn $6/shirt. How many shirts should she

plan to buy? e. If Malia is then able to sell every shirt she purchases, how much money will she raise?



3. Hoku invested some money in a stock on Jan 1, 2005. The following graph shows the value of the

stock, in dollars per share, over time.

Val

ue

48 36 24

12

0

2 4 6 8

Years since Jan 1, 2005 a. What was the initial value of Hoku’s stock? b. How much was the stock worth on Jan 1, 2013? c. When was the stock worth $18/share? d. In what year did the stock return to its June 25, 2006 value? e. What was the minimum value of Hoku’s stock?

Algebra 1 – Module 4: Functions Name _______________________________ F-5.5: Stations Activity Pd ____________ Date _______________


Meet your group at your assigned station. Work together to answer the questions related to the graph. Before rotating to the next station, have your teacher check your group’s answers and make sure that everyone in your group understands the solution. Be prepared, as a group, to present your solutions to the class.

Station #1

1) 6) 2) 7) 3) 8) 4) 9) 5) 10)

Station #2

1) 6) 2) 7) 3) 8) 4) 9) 5) 10)

Station #3

1) 6) 2) 7) 3) 8) 4) 9) 5) 10)



Station #4

1) 6) 2) 7) 3) 8) 4) 9) 5) 10)

Station #5

1) 6) 2) 7) 3) 8) 4) 9) 5) 10)

Station #6

1) 6) 2) 7) 3) 8) 4) 9) 5) 10)



Part I: Warm-up (follow your teacher’s instructions) For the graph below,

• the scale used on the x-axis is 1 unit;

• the scale used on the y-axis is 20 units.

• What do you notice about the graphs?

• What information can you get just from looking at the graph?

• What might the story of this graph be?



Part II: Answer the questions for each graph provided. 1) The following graph shows Kimo’s speed, in miles per hour, during a hike at Volcano National Park.

S

peed

(mph

)

4 3 2 1 0

30 60 90 120

Time (min) a. How fast did Kimo initially start walking? b. How long did it take Kimo to finish his hike? c. Approximately how fast was Kimo hiking 90 minutes into his hike?

d. What was Kimo’s maximum speed during his hike?

e. How many minutes into his hike did Kimo reach his maximum speed?

f. During what time period(s) was Kimo hiking at a steady speed?

g. During what time period(s) was Kimo stopped.



2. The graph below shows a museum’s projected annual profit P(c), in thousands of dollars, as a

function of the cost c, in dollars, of an admission ticket. P(c)

Ann

ual P

rofit

(10

00’s

of d

olla

rs)

120 90 60 30

0

c 12 24 36 48

Cost of one ticket a. How much money can the museum expect to make if they don’t charge for admission?b. What is the value of P(9)? Explain the meaning of your answer in context. c. For what value(s) of c does P(c) = 105,000? Explain the meaning of your answer(s) in context. d. How much should the museum charge for admission to maximize their profit? e. What is the maximum profit the museum can expect? f. Approximately what is the maximum amount the museum can charge for admission before they

stop making a profit?



3. The following graph approximates the rate (in people per min) at which students are entering (E) and

leaving (L) the gym t minutes after the start of a basketball game.

N

umbe

r of P

eopl

e pe

r Min

80 60 40 20 0

L E

10 20 30 40 Time (minutes)

a. At what rate are people leaving the gym at the start of the game? b. At what rate are people entering the gym at the start of the game? c. After how many minutes are people entering the gym at a rate of 60 people per min? d. After how many minutes are people leaving the gym at a rate of 10 people per min? e. After how many minutes does the number of people in the gym reach a maximum? Provide a brief

explanation to justify your answer. f. Over what time period is the number of people in the gym increasing? Provide a brief explanation

to justify your answer. g. Over what time period is the number of people in the gym decreasing? Provide a brief explanation

to justify your answer.



Part III: Reflect and summarize (follow your teacher’s instructions)

Algebra 1 – Module 4: Functions Name _______________________________ F-6.1: Interpreting the Shape of a Graph Pd ____________ Date _______________


Part I: Warm-up (follow your teacher’s instructions) 1. Determine a context for the graph below and label the axes appropriately for the situation you

decide to use. Use the space below to describe the scenario for your context.

2. Create 5 questions that can be answered using the graph. Your questions should refer to a variety

of the graph’s important features (ex: intercepts, min/max values, particular points on the graph).

Questions: A.

B.

C.

D.

E.



Part II: Constant, Increasing and Decreasing Intervals

2. For each of the following, highlight/shade the regions of the graphs that correspond to different graph shapes (constant, increasing, or decreasing).

Shading: Pencil = Constant Black = Increasing Blue = Decreasing

A. B.

C. D.

E. F.



3. Cierra rides her skateboard on the street in front of her home (the road is straight and level). She

starts from in front of her home, rides to the end of her street and then turns around to head back toward her home.

The graph below represents her distance from home in relation to the amount of time since she began (t = 0 corresponds to the time she began her ride).

Usethegraphtohelpyouanswerthequestionsonthenextpage.

A

C

D E

F G

H

B

Distancetraveled

(meters)

Time(seconds)



a. What was Cierra doing between times B and C? Explain.

b. During which times was Cierra traveling away from her house? Explain.

c. During which times was Cierra going the fastest on her skateboard? Explain.

d. What was Cierra doing between points G and H? (H is the point to the farthest right on the graph.) Explain.



Part III: Producing a graph involving the distance traveled over an interval of time. 4. Keoni takes the bus to school and depending on how early or late he leaves his home, he must walk

and/or run to the bus stop in order to catch the bus. The bus stop is located on the same street that Keoni lives on, about 1 mile from his home.

For each scenario described below, sketch a graph of the function d(t) to appropriately represent the situation described.

• t represents the amount of time that has elapsed since Keoni left his home.

• d(t) represents Keoni’s distance from his home at any time t.

• t = 0 represents the time he left his home.

• For all of the graphs, except question D, the last point on your graph should represent the moment he stepped on the bus.

• Note: you do not need to label the scale for each axis. A. Keoni walks at a constant rate and arrives 10 minutes before the bus arrives.

B. Keoni is late. He runs as fast as he can until he gets tired, and then walks the rest of the way, arriving just in time to catch the bus.

Dis

tanc

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time

Dis

tanc

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time



C. Keoni walks at a constant rate until he sees his aunty coming out or her house (she lives on the same street as Keoni). Keoni talks with her for about 5 minutes, then realizes he might miss the bus, so he runs the rest of the way at a constant rate, arriving just in time to be the last one on the bus.

D. This time Keoni is really late! He runs as fast as he can all the way to the bus stop, but runs slower and slower as he gets tired. He arrives at the bus stop and after waiting there for 20 minutes he remembers that today is a holiday: Dr. Martin Luther King, Jr., Day. He runs as fast as he can back to his home, exactly the same way he ran on the way to the bus stop: he runs as fast as he can all the way back to his home, but runs slower and slower as he gets tired.

Dis

tanc

e fr

om h

ome

time

Dis

tanc

e fr

om h

ome

time



E. Keoni is early today, so he walks at a leisurely rate. About a quarter of the way to school he realizes

he forgot his math homework, again! He walks briskly back home, but about halfway back home he remembers he didn’t have math homework, so he walks even faster to the bus stop, arriving about 1 minute before the bus arrives.

F. Keoni has plenty of time to get to the bus. He walks slowly for a while, and then stops to watch a gecko chase a bug. He continues at a slightly faster pace for a while longer and stops again, this time to tie his shoe and watch a man unload tools from his truck. He realizes he’s possibly late now and continues at a still faster pace until he arrives just in time to catch the bus.

Part IV: Reflect and Summarize (follow your teacher’s instructions)

Dis

tanc

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time

Dis

tanc

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time

Algebra 1 – Module 4: Functions Name _______________________________ F-6.2: Interpreting Graphs Showing Change Over Time Pd ____________ Date _______________


Part I: Warm-up 1. Solve the following equation: 2. Solve the following inequality:

1312x +15( )− 5x − 4 = x +3 x

5+10 >1

3. Write a sentence/question to translate the following equation into words (do not solve the equation,

simply translate it into a question): x2 +100 =1000 4. Write an algebraic expression to represent the quantity that is being described: A new online streaming video company charges a one-time membership fee of $21 to join plus $3 for every movie you watch. 5. Follow your teacher’s instructions.



Part II: Water is poured into the following containers at a constant rate. Match the graphs below, which represent the height of the water at time t, with the containers above. Assume t = 0 corresponds to the time when the water began entering each of the containers, the scales on all graphs are the same, and that the rate at which the water entered the containers was the same. Explain why you chose each one and why the other graphs do not work for each container. 1.

2.

3.

4.

5.

A BC

D



Part III: Circle the graph that best represents the below scenarios. 6. A school bus drives 30 miles per hour for a while and then pulls into the school and lets off students.

Which graph best represents the bus’s speed as a function of time? A. B. C. D.

7. A bungee jumper jumps off a 100-foot high bridge. Which graph best represents her height from the

ground as a function of time? A. B. C. D.

8. A bicyclist climbs up a hill at a steady pace of 10 miles per hour and then speeds up as she glides

down the other side. Which graph best represents her speed as a function of time? A. B. C. D.



9. An anteater at the zoo is given ants for lunch. He slowly eats 4 ants and takes a break, repeating this

pattern throughout lunch. Which graph best represents the number of ants remaining as a function of time?

A. B. C. D.

10. A lawn service mows the grass every three weeks. Which of the below graphs best represents the

height of the grass as a function of time? A. B. C. D.

Algebra 1 – Module 4: Functions Name _______________________________ F-6.3: Graphing Stories Pd ____________ Date _______________


Part I: Follow your teacher’s instructions. 1. Title: ___________________________________________

Lab

el fo

r y-

axis

: __

____

____

____

____

____

____

_

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Time (seconds)

2. Title: ___________________________________________

Lab

el fo

r y-

axis

: __

____

____

____

____

____

____

_

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Time (seconds)



3. Title: ___________________________________________

Lab

el fo

r y-

axis

: __

____

____

____

____

____

____

_

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Time (seconds)

4. Title: ___________________________________________

Lab

el fo

r y-

axis

: __

____

____

____

____

____

____

_

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Time (seconds)



Part II: Reflect and Summarize (follow your teacher’s instructions).

Algebra 1 – Module 4: Functions Name _______________________________ F-6.4: Graphing Scenarios with more Precision Pd ____________ Date _______________


Part I: Warm-up 1. The graph below shows the distance Sue traveled as she was returning home from somewhere.

Three students each provided a different description of what happened during Sue’s travel (based on the graph provided above).

• First, circle either “Match” or “No Match” to indicate if the description accurately represents the graph.

• Then, provide a brief explanation to justify your selection.

A) Sue biked for 3 minutes, then took a break for 2 minutes and then was picked up by a friend who drove her 5 miles home.

Match No Match

Justification:

B) Sue drove for 4 minutes, stopped to talk to a friend for 3 minutes and then walked for 1 minute.

Match No Match Justification:

C) Sue biked for 4 minutes, took a 3-minute break, and then was picked up by a friend who drove her the final 2 miles home.

Match No Match

Justification:

Time (minutes)

Distance (miles)



Part II: Creating more precise graphs For the following situations, create a graph that is as precise as possible (i.e., consider actual numerical values for the given context). Also, provide labels and indicate the scale for the x-axis and the y-axis. 2. Kim is filling a rectangular container (shown below) at a rate of 15 cubic meters per minute for the

first six minutes. Then, she increased the flow rate to 20 cubic meters per minute. Sketch the height of the water h(t) as a function of time t.

Lab

el fo

r y-

axis

: ___

____

____

____

__

Label for x-axis: _________________



3. Jim filled a water tank (shown to the right) at a rate of 4 cubic meters per minutes for 6 minutes. He then turned off the water and took a break for 2 minutes. When he returned to fill the tank, it only took 1 minute. Sketch the height of the water h(t) as a function of time

Lab

el fo

r y-

axis

: ___

____

____

____

__

Label for x-axis: _________________

4. Grass grows about 1 inch per week during the summer. Sam usually mows your lawn down to 1 inch every two weeks (so during Week 2,4,6, etc.). In the 4th week of the summer, Sam went on vacation and did not mow your lawn that week. If your lawn started off at a height of 1 inch at the beginning of the summer (Week 0), graph the height H(t) of the grass as a function of time t for the 10 weeks of summer.

Lab

el fo

r y-

axis

: ___

____

____

____

__

Label for x-axis: _________________



Part III: Reflect and summarize. 5. Choose dimensions for the rectangular prism below.

• Use “feet” for the units for each dimension of the prism.

• Choose two rates, in cubic feet per minute ( ft.3

min.) that you would like to work with.

o To fill the first half of the container, water will be pumped into the container at the rate you select for “rate 1”.

o Then, to fill the second half of the container, water will be pumped into the container at the rate you select for “rate 2”.

Create a graph that shows the volume of water in the container over time. Label the axes and

indicate the scale used for each axis.

L W

H

Dimensions of the container: L: length = _____________________

W: width = _____________________

H height = _____________________

Water will be pumped into the container at the following rates: Rate 1 (to fill the first half of the container): _____________________

Rate 2 (to fill the second half of the container): _____________________

Lab

el fo

r y-

axis

: ___

____

____

____

__

Label for x-axis: _________________



1. Iris is in a hotdog eating contest. She decides to use a particular strategy:

• She starts by eating 5 hotdogs in the first minute and then takes a 1-minute break. • Then, she eats 2 hotdogs in one minute and then takes a 30 second break. • Then, she eats 2 more hotdogs in one minute and then takes another 30 second break. • She keeps repeating the last step above (2 hotdogs in one minute followed by a 30 second

break) until time is called. • This year, she ate a total of 17 hotdogs.

a. Sketch a graph representing the number, N(t), of hotdogs she has eaten as a function of time, t.

Ø Provide labels for both axes and indicate the scale for both axes.

Lab

el fo

r y-

axis

: ___

____

____

____

__

Label for x-axis: _________________

b. If she were allowed to continue eating, how long would it take her to eat 25 hotdogs?



2. You have a $1200 loan that you want to pay off (with no interest). You make the following

agreement with the lender to pay back the money you owe:

• At the end of the first month, you will pay $300. • Then, you will pay $150 each month until the debt is paid off.

a. Draw a graph of the amount of the loan left to repay, A(t), as a function of time.

Ø Provide labels for both axes and indicate the scale for both axes.

Lab

el fo

r y-

axis

: ___

____

____

____

__

Label for x-axis: _________________

b. How long will it take you to pay off the loan?

Algebra 1 – Module 4: Functions Name _______________________________ F-6.6: Distance, Rate and Time Pd ____________ Date _______________


Part I: Warm-up 1. Determine the solution for each of the following.

A. 1= 25 x + 2( )− x B. x − 5≥ 23x + 6

Follow your teacher’s instructions to take some notes to review distance, rate and time.



Part II: The relationship between distance, rate and time

2. Answer the following questions using the formula d = rt (the total distance traveled is the product of the rate you traveled at and the length of time you traveled at that rate).

a. Andy sprinted down a football field at a rate of 20 feet per second for 25 seconds. How far did he run?

b. Kelli drove on a highway in California for 2 hours without stopping. She traveled a total of 115

miles. What is the (average) rate she traveled at? c. Superman threw a ball and it landed 3 miles away. If the (average) rate that the ball traveled at

was 200 feet per second, how long did it take for the ball to land? 3. A truck leaves the warehouse and the driver travels for 3 hours at 20 miles per hour. Then, the

driver stops at a truck stop for 30 minutes. After that the driver gets back on the highway and drives another 3 hours at 60 miles per hour. Graph the total distance the driver traveled D(t) as a function of time, t. Label your axes (titles and scales/units).

Lab

el fo

r y-

axis

: ___

____

____

____

__

Label for x-axis: _________________



Part III: Biking home from school (Trina’s and Kimo’s journeys) 4. Trina bikes home from school every day. Her house is 6 miles from the school. She leaves school at

3:00 pm and rides for 15 min at 0.2 mi/min. Then she stops for 10 min to talk to a friend. She is reminded that she forgot a book at school and hurries back there at 0.6 mi/min. She grabs her book and bikes the rest of the way home at 0.3 mi/min. Sketch two graphs as indicated below.

A. Distance from School vs. Time

B. Total Distance Traveled vs. Time



5. Kimo bikes home from school every day. His house is 7 miles from school. He leaves at 4:00pm and rides for 10 min at 0.2 mi/min. He looks at the time and doubles his speed for the next 2 miles. He gets tired and stops at 7-11 for 5 min to grab some water. While there he remembers that he needed to turn in a math assignment. It takes him 10 min to bike back to school. He turns in the assignment and makes it back home in 20min. Sketch two graphs as indicated below.

A. Distance from School vs. Time

B. Total Distance Traveled vs. Time



Part IV: Reflect and Summarize 6. Describe the differences between the Distance from School vs. Time graphs for Kimo’s and Trina’s

journeys.

7. Describe the differences between the Total Distance vs. Time graphs for Kimo’s and Trina’s journeys.

8. Describe the differences in both students’ journeys. Consider and respond to the following: • Who traveled farther? Explain your answer. • Who traveled for a longer period of time? Explain your answer.

Algebra 1 – Module 4: Functions Name _______________________________ F-7.1: Linear Functions Revisited Pd ____________ Date _______________


Part I: Follow your teacher’s instructions



Part II: Review of linear functions Consider the graph shown below.

1. What appears to be the y-intercept of the graph? ______________ 2. The graph actually represents the function 𝑓 𝑥 = 7

%𝑥 + %

7 . Verify the y-intercept by determining the

value of f(0). 3. What is the slope of the graph of f(x)? 4. In the coordinate plane provided above, graph all 3 of the following functions: a. k(x) = 4 b. m(x) = -3.5 c. p(x) = 0 5. For all 3 functions above (in question 6), what is the slope of each line? 6. How would you describe the graphs of all 3 functions in question 6? 7. In general, any function in the form f(x) = b, the graph will be a _____________________ line, the

slope of the graph will be _____________ and the y-intercept will be ______________.



Part III: Division by zero 8. To determine the value of the following expressions we simply divide the numerator by the

denominator. Determine the value of each of the expression.

A. 123

B. −355

C. 07

D. −8−8

E. 50

F. −30

9. Compare your answers with a partner and then discuss the following:

A. How could you check to make sure your answer for 8A is correct? Write an equation below that can be used to verify that your answer is correct.

B. How could you check to make sure your answer for 8B is correct? Write an equation below that can be used to verify that your answer is correct.

C. Another student in your class just said aloud that the answers for 8E and 8F are both zero. The following is what he wrote on his paper:

50

= 0 −30

= 0

Check to see if his answers are correct. Write an equation for each to verify whether his answers are correct or not.

10. Use the space below to take some notes regarding “division by zero” (follow your teacher’s

instructions).



Part IV: The graph of x = c

11. The following equations can be represented by a line graphed in the coordinate plane. Complete the table of values for each equation and use your table to create the graph.

A. x = 4 B. x = −3 12. Discuss with a partner what you notice about each table of values and its corresponding graph.

Write down some of the ideas that you discussed. 13. Determine the slope of each line you graphed in question #11 above. A. x = 4 B. x = −3

x y 3 2 1 0 -1

4 4

x y 3 2 1 0 -1

-3 -3



14. Graph each pair of equations in the same coordinate plane. Use a table of values to help you

identify a few points that will lie on each graph. A. x = 2 and f (x) = 2 B. x = −5 and f (x) = −5 Part V: Reflect and Summarize (follow your teacher’s instructions).



1. Determine the value of each of the following expressions.

A. 1005

B. 80

C. 012

D. −3.14−3.14

E. −130

F. 40

2. Graph each equation or function. If necessary, use a table of values to help you identify a few

points that will lie on each graph. A. x = 6 B. f (x) = 4 C. x = −2 D. g(x) = −3



3. Each pair of functions is written in slope-intercept form: f(x) = mx + b.

• State the slope and the y-intercept of each function.

• Then, graph the pair of functions in the same coordinate plane.

A. f (x) = 2x − 5 and g(x) = −1

B. p(x) = −13x +3 and r(x) = 2

Algebra 1 – Module 4: Functions Name _______________________________ F-7.3: Absolute Value Pd ____________ Date _______________


Part I: Review of Absolute Value (follow your teacher’s instructions to take notes).

Ø Definition

Ø How to write it

Ø Some examples Part II: Absolute Value Expressions Determine the value of each expression. 1. 54 2. − −3 3. −3+ 2 4. −10− 20 5. 15− (−20) 6. − 23+ 23 7. Write 3 different absolute value expressions that all have a value of 7.



Part III: Graphing absolute value functions. 8. The most basic absolute value function is 𝑓 𝑥 = |𝑥|. Create the graph of this function by

completing the table below and graphing the ordered pairs on the coordinate plane.

9. Talk to your partner about the graph you drew. What do you notice about its shape, slope, etc.?

Just discuss the graph (you don’t have to write anything down). 10. Create the graph of each of the following absolute value functions by completing a table of values

and graphing the ordered pairs in the coordinate planes. A. f (x) = x − 2

x f(x)

-3

-2

-1

0

1

2

3

x f(x)

-1

0

1

2

3

4

5



B. g(x) = x + 4

C. h(x) = x +1

D. k(x) = x −3

x g(x) -6 -5 -4 -3 -2

x h(x) -4 -3 -2 -1 0 1 2

x k(x) 0 1 2 3 4 5 6



11. Graph the following absolute value functions in the same coordinate plane (provided below).

• First, complete the table of values for each function.

• Then, plot the ordered pairs and sketch the graph through those points.

• Note: the graph of f (x) = x is already provided (simply as a reference).

A. p(x) = 2 x B. q(x) = 3 x C. r(x) = 12x

x p(x) -3 -2 -1 0 1 2 3

x q(x) -2

-1

0

1

2

x r(x)

-4

-2

-1

0

1

2

4

Algebra 1 – Module 4: Functions Name _______________________________ F-7.4: Solving Equations Graphically Pd ____________ Date _______________


Part I: Warm-up

1. Trevor is a waiter at a restaurant in Waikiki. The table below shows the number of hours he worked each week (for the past two months) and the amount of money he earned from tips that week.

A. Create a scatter plot of the data set. Provide a label and indicate the units for each axis. B. Sketch a line of best for your scatter plot and then determine the function that represents your

line of best fit. Write your function in slope-intercept form. C. Explain what the slope of your function represents in the context of the given situation. D. Translate the statement f(9) = 144 into a sentence (in words) using the context of the given

situation. E. The statement f (x) = 345 is actually asking you a question. Write the question (in words)

using the context of the given situation, and then use either the table or the graph to answer your question.

F. Use your function to determine how much money Trevor could expect to earn from tips if he

worked 30 hours in one week.

Hours Worked

Amount Earned from Tips ($)

17 298 10 135 21 345 9 144 16 250 13 167 16 218



Part II: Seeing an equation as two functions set equal to each other: f (x) = g(x)

2. Identify the two functions that are embedded in each of the following equations.

A. 3x + 4 = x − 2 B. 2−3x = −4x +1 C. 52x = x + 6

f(x) = _____________ f(x) = _____________ f(x) = _____________ g(x) = _____________ g(x) = _____________ g(x) = _____________

D. 2x − 7 = 5 E. 13x −3= 5 F. x +3 = 4

f(x) = _____________ f(x) = _____________ f(x) = _____________ g(x) = _____________ g(x) = _____________ g(x) = _____________ Part III: Solving equations graphically In the equation 3x + 4 = x − 2 , we need to see the opposite sides of the equation as two distinct functions: f (x) = 3x + 4 and g(x) = x − 2 Now, let’s graph both functions, f(x) and g(x), in the same coordinate plane.



3. Use the graphs of f (x) = 3x + 4 and g(x) = x − 2 (on the previous page) to help you answer the

following questions. A. What appears to the be coordinates of the point where f(x) and g(x) intersect? B. Solve the following equation algebraically (show your work): 3x + 4 = x − 2 C. Compare your answers to questions 3A and 3B to each other. What do you notice about the solution

to the equation 3x + 4 = x − 2 in relation to the coordinates of the point where f(x) and g(x) intersect?

Part IV: Use the space below to take some notes about solving equations graphically (follow your teacher’s instructions). 4. 3x + 2 = 2x + 4 5. 2x +3= 5



6. 12x −1= 2 7. x +3 = 4

8. x − 2 = 2 9. 3 x = 6



1. The function g(x) = −3x +1 is graphed in the coordinate plane below (the scale used on each axis is

1 unit). Use the graph of g(x) to help you determine the solutions to the following equations.

2. The function 𝑐 𝑥 = 𝑥 − 4 is graphed in the coordinate plane below (the scale used on each axis

is 1 unit). Use the graph of c(x) to help you determine the solutions to the following equations.

A. B. C. D.

A. |𝑥 − 4| = 5 B. |𝑥 − 4| = 1 C. |𝑥 − 4| = 7

Algebra 1 – Module 4: Functions Name _______________________________ F-7.6: Solving Quadratic Equations Graphically Pd ____________ Date _______________


Part I: Warm-up

1. Determine the equation of the line that goes through the points ( 21, 345 ) and ( 16, 250 ). 2. Makana started a new fitness program. The table of values below represents a linear function

showing the maximum weight that she is able to bench press at the end of each week that she is in the program.

Part II: Quadratic Equations So far we’ve primarily worked linear equations (e.g., 2x +3= 4 ) and recently we learned about absolute value equations (e.g., x + 4 = 6 ). Now we’re going to begin working with another category of equations. Consider the equation x2 − 4 = 5

• This is called a quadratic equation; you will learn how to solve this type of equation

algebraically later in this course.

• Since we don’t yet know how to solve a quadratic equation using algebraic methods, we will have to solve it graphically.

Week Maximum bench press weight (lbs.)

1 87

2 92

3 97

4 102

5 107

6 112

7 117

A. Determine the linear function, f(x), that represents the data shown in the table.

B. Explain the meaning of the slope of your

function in the context of the given situation.



Just as we did in the previous lesson, when we want to solve an equation graphically, we want to see the equation as having two functions, one on each side of the equation: f (x) = g(x) . 3. In the equation x2 − 4 = 5 , what are the functions that are on each side of the equation? f (x) = _____________ and g(x) = _____________ 4. Below is the graph of the function f (x) = x2 - 4. The scale used on each axis is 1 unit.

A. Graph g(x) in the coordinate plane below.

B. On the graph, mark the two points where f(x) and g(x) intersect. C. State the x-coordinate of each point that you marked: ______________ and ______________ D. These x-coordinates are the solutions to the original equation 𝑥7 − 4 = 5. Verify that these

solutions are correct by evaluating f(x) at each x-coordinate you stated above.



5. Determine the solution to the following equations.

• The function on the left side of each equation, f (x) = x2 − 4 , is graphed in the coordinate plane above. The scale used on each axis is 1 unit.

• For each equation below,

• state a function for g(x) and graph it in the coordinate plane above;

• mark the points where f(x) and g(x) intersect;

• state the x-coordinate of the point(s) of intersection;

• verify the solutions by evaluating f(x) at both values.

A. x2 − 4 = −3 B. x2 − 4 = 0 C. x2 − 4 = −4



6. Use the graph of f (x) = x2 − 4

to approximate the solutions to the following equations.

A. x2 − 4 = 3 B. x2 − 4 = −2 C. x2 − 4 = 6 7. Use the graph of f (x) = x2 − 4 to help you explain why the equation x2 − 4 = −5 has no solution. Part III: Reflect and Summarize (follow your teacher’s instructions).



1. P(x) = x2 − 6x +8 is graphed in the coordinate plane below. The scale used on each axis is 1 unit. Use the graph of P(x) to help you determine the solutions to the following equations. If any solutions

are not integers, approximate the solution to the nearest tenth. A. x2 − 6x +8 = 3 B. x2 − 6x +8 = −1 C. x2 − 6x +8 = 2 D. x2 − 6x +8 = 0 E. x2 − 6x +8 = 6 F. x2 − 6x +8 = 8 G. Explain why x2 − 6x +8 = −2 has no solution.



2. A(x) = −x2 + x +8 is graphed in the coordinate plane below. The scale used on each axis is 1 unit. Use the graph of A(x) to help you determine the solutions to the following equations. If any solutions

are not integers, approximate the solution to the nearest tenth. A. −x2 + x +8 = 0 B. −x2 + x +8 = −1 C. −x2 + x +8 = 6 D. −x2 + x +8 = 4 E. Explain why −x2 + x +8 = 9 has no solution.



At each of the stations, use the graph to solve each of the given equations. If an equation has no solution, write “No solution” and explain why no solution exists. Station 1 x2 −36 = 0 x = _______________ x2 −36 = −20 x = _______________ x2 −36 = 20 x = _______________ Station 2 12x −3 = 3 x = _______________

12x −3 = 0 x = _______________

12x −3 =1 x = _______________

Station 3 2x −14 = −6 x = _______________ 2x −14 = 0 x = _______________ 2x −14 = −16 x = _______________



Station 4 x2 − 9 =16 x = _______________ x2 − 9 = −11 x = _______________ x2 − 9 = −8 x = _______________ Station 5 74x − 5= 2 x = _______________

74x − 5= 9 x = _______________

74x − 5= −5 x = _______________

Station 6 2 x + 4 = 5 x = _______________ 2 x + 4 = 9 x = _______________ 2 x + 4 =1 x = _______________



1. Determine the value of each expression.

A. −75 B. −15025

C. 40

D. 5

E. 025

F. −100− 900 G. 07

H. 540

2. Graph each pair of equations in the same coordinate plane. Use a table of values to help you

identify a few points that will lie on each graph. A. x = 3 and f (x) = 3 B. x = −4 and g(x) = −4



3. Graph the function h(x) = x + 5

4. Use the graph you created in question 3 (above) to solve the following equation. Explain how you determined your solution.

x + 5 = 4 5. Determine the solution to x2 + 2x +1= x +3 . The scale used on each axis is 1 unit.

x h(x) -8 -7 -6 -5 -4 -3 -2

Algebra 1 – Module 4: Functions Name _______________________________ F-8.1: Inequalities in Context Pd ____________ Date _______________


Athletes train year-round for the annual Ironman World Championship in Kailua-Kona. Many of the athletes use heart rate monitors while they train to better prepare their bodies for the grueling race.

The ironman athletes try to keep their heart rate at or below their target heart rate.

• Knowing your “target heart rate” helps you to get the most benefit when exercising. If you exceed your target heart rate, you are exercising at a very high intensity and may be over doing it. If you are way below your target heart rate you may not be exercising hard enough to get any significant benefits.

• In general (e.g., if you were going to a gym to exercise by running on a treadmill), to find your target heart rate, you subtract your age from 220. The result is the number of beats per minute your heart should be beating when you are at your target heart rate.

• However, due to the specialized training required for ironman athletes, many of them use the following method to determine their target heart rate: they subtract their age from 180 (resulting in a measure of beats per minute, or bpm).

1. Consider the specialized training required for ironman athletes. If T represents an ironman athlete’s target heart rate and a represents his/her age (in years), write the symbolic form for the function T(a) that represents the target heart rate for any age.

2. Use your function to determine the following values and briefly explain what your answer means in

the context of the given situation.

a. f(45) b. f(21) 3. Use your function to determine what age an athlete would have the following target heart rates:

a. 123 bpm b. 146 bpm 4. Graph T(a) in the coordinate plane below and use the graph to answer the questions that follow.

Lab

el fo

r y-

axis

: ___

____

___ During training, ironman athletes try to keep their

actual heart rate at or below their target heart rate.

a. What heart rates would be acceptable for a 25-year-old ironman athlete?

b. Is a heart rate of 146 acceptable for a 35-year-old ironman athlete? Explain why or why not.

Label for x-axis: _________________

Algebra 1 – Module 4: Functions Name _______________________________ F-8.1: Inequalities in Context Pd ____________ Date _______________


Young Surfboard Designs shapes surfboards for local pros on the North Shore. Owen Young owns the company and he charges a flat fee of $500 for a 5’11” surfboard. He then charges an extra $10 per additional inch.

1. Write the symbolic form for the cost C(x) that Young charges for shaping a surfboard x inches longer than 5’11”.

2. Graph C(x) in the coordinate plane below. Label your axes with a title and units.

3. What is the cost of shaping a 6’6” surfboard? Mark the point on your graph that represents this cost.

4. Kalani has a budget of $660. He cannot spend more than that on his surfboard. Write an inequality that models this restriction.

5. Solve the inequality to determine the longest surfboard Kalani can purchase.

Algebra 1 – Module 4: Functions Name _______________________________ F-8.2: Solving Inequalities Graphically Pd ____________ Date _______________


Part I: For each of the following graphs for f (x), shade the portion of the x-axis corresponding to x values for which f (x) > 0. (Remember, x-coordinates on a graph correspond to function inputs, and y-coordinates correspond to function outputs.) Write the solution below the graphs using set notation. 1. 2.

f (x) > 0 for ____________________ f (x) > 0 for ____________________ 3. 4.

f (x) > 0 for ____________________ f (x) > 0 for ____________________



Part II: For each of the following graphs for f (x), shade the portion of the x-axis corresponding to x values for which f (x) < 0. (Remember, x-coordinates on a graph correspond to function inputs, and y-coordinates correspond to function outputs.) Write the solution below the graphs using set notation. 5. 6.

f (x) < 0 for ____________________ f (x) < 0 for ____________________ 7. 8.

f (x) < 0 for ____________________ f (x) < 0 for ____________________



Part III: For the next two graphs of f (x), shade the portion of the x-axis that indicates those x-values for which f (x) < 6. Write the solution below the graphs using set notation. 9. 10.

f (x) < 6 for ____________________ f (x) < 6 for ____________________ Part IV: For the next two graphs of f (x), shade the portion of the x-axis that indicates those x-values for which f (x) > -4. Write the solution below the graphs using set notation. 11. 12.

f (x) > -4 for ____________________ f (x) > -4 for ____________________



Part V: For the next two graphs of f (x), shade the portion of the x-axis that indicates those x-values for which f (x) < 0. Write the solution below the graphs using set notation. 13. 14.

f (x) < 0 for ____________________ f (x) < 0 for ____________________ Part VI: For the next two graphs of f (x), shade the portion of the x-axis that indicates those x-values for which f (x) > 0. Write the solution below the graphs using set notation 15. 16.

f (x) > 0 for ____________________ f (x) > 0 for ____________________



At each of the stations, use the graph to solve one the given equations. If an equation has no solution, write “No solution” and explain why no solution exists. Station 1 𝑥7 − 36 < 0 ___________________________________ 𝑥7 − 36 < −20 ___________________________________ 𝑥7 − 36 > −20 ___________________________________ Station 2 𝑥7 + 𝑥 − 6 < 0 ___________________________________ 𝑥7 + 𝑥 − 6 > 0 ___________________________________ 𝑥7 + 𝑥 − 6 < −6 ___________________________________ Station 3 2𝑥 − 14 < 0 ___________________________________ 2𝑥 − 14 > 0 ___________________________________ 2𝑥 − 14 > −8 ___________________________________



Station 4 𝑥7 − 9 < 16 ___________________________________ 𝑥7 − 9 < 0 ___________________________________ 𝑥7 − 9 > 0 ___________________________________ Station 5 𝑥7 + 4𝑥 − 5 < −8 ___________________________________ 𝑥7 + 4𝑥 − 5 < 0 ___________________________________ 𝑥7 + 4𝑥 − 5 > 0 ___________________________________ Station 6 𝑥% + 2𝑥7 + 𝑥 − 4 > 0 ___________________________________ 𝑥% + 2𝑥7 + 𝑥 − 4 < 0 ___________________________________ 𝑥% + 2𝑥7 + 𝑥 − 4 > −4 ___________________________________



Station 7 𝑥7 − 2𝑥 − 15 < 0 ___________________________________ 𝑥7 − 2𝑥 − 15 > 0 ___________________________________ 𝑥7 − 2𝑥 − 15 < −12 ___________________________________ Station 8 𝑥7 − 25 < 0 ___________________________________ 𝑥7 − 25 < −16 ___________________________________ 𝑥7 − 25 > −16 ___________________________________ Station 9 𝑥7 − 𝑥 − 2 < 0 ___________________________________ 𝑥7 − 𝑥 − 2 < −2 ___________________________________ 𝑥7 − 𝑥 − 2 > −2 ___________________________________

Vocabulary


A – B – C:

D – E – F:

Vocabulary


G – H – I:

J – K – L:

Vocabulary


M – N – O:

P – Q – R:

Vocabulary


S – T – U – V:

W – X – Y – Z:

Blank Pages for Notes and Scratch Work


Algebra 1 Q2 Packet - Maui High School

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Transcript of Algebra 1 Q2 Packet - Maui High School