STUDY GUIDE- Summative #1- Functions Name _____________________________

F-1 to F-4 Per _____ Date _____________________

M.1- Understand the Concept of a Function and use Function Notation

F (0-1) C (2-2.75) B (3-3.25) A (3.5-4)
There is LITTLE OR NO The student OCCASIONALLY The student USUALLY The student CONSISTENTLY
Rubric ATTEMPT to show/demonstrate demonstrates an understanding demonstrates an understanding of demonstrates an understanding of
understanding of the outcome. of the outcome. the outcome. the outcome.
Range 0-69% of the Success Criteria 70-79% of the Success Criteria 80-89% of the Success Criteria 90-100% of the Success Criteria
______ Identify the meanings of x and f(x) in context
Success ______ Write a given statement in function notation
Criteria ______ Determine the value of an input or output given a table
______ Determine whether this value makes sense in this context and explain why or why not.

M.2- Interpret function that arise in applications in terms of context

F (0-1) C (2-2.75) B (3-3.25) A (3.5-4)
There is LITTLE OR NO The student OCCASIONALLY The student USUALLY The student CONSISTENTLY
Rubric ATTEMPT to show/demonstrate demonstrates an understanding demonstrates an understanding of demonstrates an understanding of
understanding of the outcome. of the outcome. the outcome. the outcome.
Range 0-69% of the Success Criteria 70-79% of the Success Criteria 80-89% of the Success Criteria 90-100% of the Success Criteria
______ Create an ordered pair that makes the makes the table not represent a function
______ Explain why a table does not represent a function
______ Create a graph that’s not a function
______ Explain why a graph does not represent a function
______ Use the graphical representation of a function to verify its symbolic representation by showing that points on the graph are solutions to
Success the equation y=f(x)
_____Determine if the graph matches the symbolic representation
Criteria
_____ Justify or Explain your reasoning
_____ Evaluate which representation is easiest and most appropriate to use based on the information given, the context, and the question asked
_____ Use a symbolic, table or graph representation of a function to answer a question about a given scenario.
_____ Select a representation to answer a question about a scenario and explain why you chose that representation.
______ Fill in a table that represents a function
______ Transfer a table of values to a graph

1. Add an ordered pair to the table so that the 2. Add an ordered pair to the table so that the
representation is NOT a function. Briefly representation is a function. Briefly explain why
explain why the representation is not a function. the representation is not a function.

x y x y
-5 4 3 9
8 0 -2 -1
1 2 5 0
-4 -2 -1 8

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STUDY GUIDE- Summative #1- Functions Name _____________________________
F-1 to F-4 Per _____ Date _____________________

3. Sketch a graph that is NOT a function. Briefly 4. Sketch a graph that is a function. Briefly
explain why the representation is not a function. explain why the representation is a function.

5. Lisa is trying to save money for college. She currently has $1000 in her savings account. She gets a job at a
local restaurant and decides to start depositing a $100 of her earnings each week. The function 𝑺(𝒘) =
𝟏𝟎𝟎𝒘 + 𝟏𝟎𝟎𝟎 represents the money she has in her savings account after 𝒘 weeks.

a) Explain what 𝑆(5) = 1500 means in the context of the situation.

b) Write the following statement using function notation:

After 12 weeks, Lia has $2200 in her savings account.

6. Mana is trying to save money for college. He currently has $2100 in his savings account. He gets a job at a
local grocery store and decides to start depositing a $60 of his earnings each week. The function 𝑺(𝒘) =
𝟔𝟎𝒘 + 𝟐𝟏𝟎𝟎 represents the money he has in his savings account after 𝒘 weeks.

a) Explain what 𝑆(6) = 2460 means in the context of the situation.

b) Write the following statement using function notation:

After 20 weeks, Mika has $3300 in her savings account.

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STUDY GUIDE- Summative #1- Functions Name _____________________________
F-1 to F-4 Per _____ Date _____________________

7. Does the symbolic representation match the graph shown? If yes, use two points to justify the match. If no,
explain why not.

Graph: Symbolic:
𝑓(𝑥) = 𝑥 2 + 2𝑥 + 3

a. Match? (circle one) YES NO

b. Justify/Explain:

8. Does the symbolic representation match the graph shown? If yes, use two points to justify the match. If no,
explain why not.
Graph: Symbolic:
𝑓(𝑥) = 𝑥 2 − 8𝑥 + 12

a. Match? (circle one) YES NO

b. Justify/Explain:

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STUDY GUIDE- Summative #1- Functions Name _____________________________
F-1 to F-4 Per _____ Date _____________________

9. Sasha is training for the Ironman triathlon and plans to spend the day riding her bicycle with her training
partner Kayla. She first drives to Kayla’s house with her bike. The following functions (symbolic, graph, and
table) all represent the distance, D(t), in miles that Sasha is from her house as a function of time, t, in hours
after the girls start their ride.

Symbolic: Graph:

Distance from Sasha’s house (in miles)

𝐷(𝑡) = 16𝑡 + 8

Table:

t D(t)
0 8
1 24
1.5 32
2.5 48

Time (in hours)

Answer each question below using either the symbolic, table, or graphical representation shown above. Indicate which
representation you used and explain why you chose to use that representation.

a) How far is Sasha from home after 0 hours?

(Include units) Symbolic / Table / Graph (circle one)

Reasoning:

b) How far is Sasha from home after 2 hours?

(Include units) Symbolic / Table / Graph (circle one)

Reasoning:

c) How far is Sasha from home after 3 hours?

(Include units) Symbolic / Table / Graph (circle one)

Reasoning:

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STUDY GUIDE- Summative #1- Functions Name _____________________________
F-1 to F-4 Per _____ Date _____________________

10. Josh is training for the Ironman triathlon and plans to spend the day riding his bicycle with his training
partner Keahi. He first drives to Keahi’s house with his bike. The following functions (symbolic, graph, and
table) all represent the distance, D(t), in miles that Josh is from his house as a function of time, t, in hours
after the boys start their ride.

Symbolic: Graph:

Distance from Josh’s house (in miles)

𝐷(𝑡) = 14𝑡 + 9

Table:
t D(t)
0 9
1 23
2.5 44
3.5 58

Time (in hours)

Answer each question below using either the symbolic, table, or graphical representation shown above. Indicate
which representation you used and explain why you chose to use that representation.
a) How far is Josh from home after 1.5 hours?
(Include units) Symbolic / Table / Graph (circle one)
Reasoning:

b) How far is Josh from home after 2.5 hours?

(Include units) Symbolic / Table / Graph (circle one)
Reasoning:

c) How far is Josh from home after 3 hours?

(Include units) Symbolic / Table / Graph (circle one)
Reasoning:

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STUDY GUIDE- Summative #1- Functions Name _____________________________
F-1 to F-4 Per _____ Date _____________________

11. Ziggy stands at an overlook that is 1000 feet above sea level. She plans to hike down a trail that will get her to the
ocean. She is confident that she can descend at a rate of 50 feet per minute.

a) Fill in the table of values representing Zoey’s height, H, above sea level as a function of time, t, in minutes after she
starts her descent.
𝑡 0 1 4 7 12 16 20 21
𝐻(𝑡)

b) What is the value of 𝐻(0) and what does it represent in context?

c) What is the value of 𝐻(7) and what does it represent in context?

d) For what value of 𝑡 will 𝐻(𝑡) = 0? Explain what your answer means in the context of the situation and why this value is
significant.

e) What is the value and meaning of 𝐻(21)? Does this make sense? Why or why not?

f) Graph the data in the coordinate plane below.

H(t)
1400
Height above sea level (ft)

1200

1000

800

600

400

200
0 2 4 6 8 10 12 14 16 18 20 t
Time (minutes)
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STUDY GUIDE- Summative #1- Functions Name _____________________________
F-1 to F-4 Per _____ Date _____________________

12. Kama stands at an overlook that is 800 feet above sea level. He plans to hike down a trail that will get him to the
ocean. He is confident that he can descend at a rate of 40 feet per minute.

a) Fill in the table of values representing Kaipo’s height, H, above sea level as a function of time, t, in minutes
after he starts his descent.
𝑡 0 1 5 6 10 14 20 22
𝐻(𝑡)

b) What is the value of 𝐻(0) and what does it represent in context?

c) What is the value of 𝐻(10) and what does it represent in context?

d) For what value of 𝑡 will 𝐻(𝑡) = 0? Explain what your answer means in the context of the situation and why this
value is significant.

e) What is the value and meaning of 𝐻(22)? Does this make sense? Why or why not?

f) Graph the data in the coordinate plane below.

H(t)
1400
Height above sea level (ft)

1200

1000

800

600

400

200
0 2 4 6 8 10 12 14 16 18 20 t
Time (minutes)
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