Unit 4 Exam 3 Functions - Comparing Functions
Ms. Tucker and Mr. Romeo
Name: ___________________________
Tentative Test Date: __________
1 Unit 4 Exam 3 Overview What is the focus of Unit 4 Exam 2? Unit 4 has continued to build on itself with each assessment. During Exam 1 of Unit 4, you identified slope (rate of change) and expanded on what you learned in 7th grade. For Exam 2, you were able to determine slope as a unit rate, compare relationships and distinguish between linear and nonlinear functions. The goal for Exam 3 is to continue expand your knowledge on functions. The goal of Exam 3 is to combine everything from the other two assessments and be able to compare rate of change (slope), initial values (y­intercept) and interpret their meaning in context from a description, graph, equation, and/or table. How will I apply what we are doing in Unit 4 Exam 2 to the future? Next year in your Algebra class you will continue to work with comparing functions from descriptions, graphs, equations, and/or tables and be required to interpret their meaning using a more algebraic approach, as well as using inequalities. What is Unit 4 Exam 2’s essential question? ● What is a function? How would you describe a function? ● How do you determine which slope is the greatest? What about initial value? What can I do at home so I am ready for the Unit 4 Exam 2 Assessment? Be able to define key terms like rate of change (slope), function, linear function, and initial value (y­intercept). Explain to your parents or a peer what each term is and how it is used in class. Show someone an example of a graph, table, equation, and description and explain to them how to determine the slope and initial value. Compare different examples and determine which one has the greatest rate of change and a greater initial value. What are some helpful resources that I can use at home and on my Chromebook? ● Check our Google classroom page that includes homework and answer keys to check your work. ● Weekly tutoring (please check with us for times). ● Review classroom notes and activities with your parent guardian at home. ● Review formative assessments and make corrections (BEFORE ASSESSMENT DATE) ● Visit M
athiaX and work on this unit’s module. What are some important side notes to remember? This is the last assessment part of Unit 4. After this assessment, we will only have 6 days until our final assessment in this unit. We will do a review at the end prior to the day of your assessment. You will receive your Learning Targets ­ Study Guide at the beginning of the unit. Remember, in order to have the opportunity to retake an assessment you must have a 70% on your formatives for this assessment period, complete the retake assignment and complete test corrections BEFORE you can retake the assessment. There will be 1­2 formatives and 1­2 homework assignments for this section. 2 Unit 4 Exam 2 Vocabulary
Word
Definition
Function
Linear Function
Slope / Rate of Change
Initial Value
Constant Rate of Change
Unit 4 Exam 2 Learning Targets Pre-Assessment
Use the “Level of Confidence” below to self-assess yourself towards this unit’s targets.
1. Novice – I don’t know where to start. I NEED HELP!
2. Developing – I don’t feel confident but I’m starting to understand.
3. Proficient – I am confident and can do it myself and show I understand.
4. Exceeds – I understand the target/skill completely and can teach others.
Target We can determine if a relationship is a function and compare their rate of change and
initial value.
Level Of Confidence Initials 3 Comparing Linear Functions and Graphs
Learning Target
We can determine if a relationship is a function and compare their rate of change and initial value.
Success Criteria
We can identify/interpret the rate of change (slope) and initial value (y-intercept) from a table, graph, equation, or description.
Essential Questions
●
● What is a function? How would you describe a function?
How do you determine which slope is the greatest? What about initial value?
Common Core State Standard
CCSS.MATH.CONTENT.8.F.1- Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set
of ordered pairs consisting of an input and the corresponding output.
CCSS.MATH.CONTENT.8.F.2 Compare properties of two functions each represented in a different way (algebraically, graphically, numerically
in tables, or by verbal descriptions
CCSS.MATH.CONTENT.8.F.3 Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of
functions that are not linear.
Each of the following examples provide information about two functions. You will use the information given to help you compare the
two functions and answer the questions about them.
1. Kayla and Janett and their friends are taking two cards to go to Six Flags from JAMS, a distance of 45 miles away. They take the
same route and drive at constant speeds. Kayla’s car begins driving at 9:00 AM and arrives at six flags at 10:20 AM. Janett’s car trip
to six flags can be represented with the equation y = 65x, where y is the distance traveled in miles and x is the time in minutes spent
traveling. Based on the two rates of change, who gets from JAMS to Six Flags faster.
Who will get to Six Flags faster? Describe in complete sentences how you determine who got to Six Flags faster.
4 2. Nayzed, Nancy, and Shakira are competing to see who can save the most money in one month, Use the table, graph, and equation
below to determine who will save the most money at the end of 30 days, Also, determine how much money each person had to start of
the competition. (Assume each is following a linear function in his or her saving habit.)
Nayzed’s Savings:
Bianca’s savings:
Shakira’s Savings
y = 2x + 20
How much money did each person have to start the competition? How did you determine each person’s initial value?
At the end of 30 days, who had the most money saved? Describe using complete sentences who had the most money saved
and what steps you took to determine your answer.
5 3. The graph below represents the distance in miles (y), Jonathan travels on his bike in minutes (x). The table represents the
distance in miles (y), Tavian travels on his bike in minutes (x). Who is traveling at a greater speed? How do you know? What
is their initial value? How do you know?
Jonathan:
Tavian:
Who is traveling at a greater speed? How do you know?
What is their initial value? How did you determine the initial value?
Questions to ask your partner…
6 The Best Cell Phone Company
T-mobile offers the following basic cell phone plan to its customers: A customer pays a monthly fee of $15.00. In addition,
the customer pays $0.05 per text message sent from the cell phone. There is no limit to the number of text messages per
month that could be sent, and there is no charge for receiving text messages.
1. If Dylan never sends a text message, what would be his total monthly cost? How did you determine the total monthly cost?
2, During a typical month, Diego sends about 100 text messages. What is his total cost for a typical month? How did you
determine the total monthly cost?
3. Mr. Romeo overdoes it on Remind and sends at least 250 text messages. What would be an estimate of the least his total
monthly cost is likely to be? Explain why this one is an estimate, not an exact amount.
4. Using the information above write a linear model (equation) describing the relationship between the number of text
messages sent and the total monthly cost.
5. How do you know the relationship between the number of text messages and total monthly cost is a linear relationship?
6. Explain what $0.05 represents in this relationship.
7. Explain what $15.00 represents in this relationship.
7 8. Sketch a graph of this relationship on the following coordinate grid. Clearly label the axis and include units in the labels.
Below are the rates for two other cell phone companies. Using the information above from T-mobile and the other two cell
phone companies, answer the following questions.
AT&T
Text Messages (input)
50
100
150
200
Monthly cost (output)
$15
$20
$25
$30
Verizon Wireless
y = 0.15x + 5
8 Which of the three companies would be the least amount of money if you never sent a single text all month? Explain how
you determined the cheapest one.
Which of the three companies would be the most amount of money if you never sent a single text all month? Explain how
you determine the most expensive one.
Which of the three companies has the cheapest charge per text? Explain how you determined your answer.
Which of the three companies has the most expensive charge per text? Explain how you determined your answer.
Comparing Linear Functions and Graphs
Questions to ask a peer about “Comparing Functions”
9 Student Self-Assessment for “What is a function?”
Use the “Level of Confidence” below to self-assess yourself towards this unit’s targets.
1. Novice – I don’t know where to start. I NEED HELP!
2. Developing – I don’t feel confident but I’m starting to understand.
3. Proficient – I am confident and can do it myself and show I understand.
4. Exceeds – I understand the target/skill completely and can teach others.
Target
We can identify/interpret the rate of change (slope) and initial value (y-intercept) from a table, graph,
equation, or description.
Level Of Confidence
Initials
10