Relations, Tables, Graphs and Functions Project
This project is designed to assess your knowledge and abilities to create tables and graphs
and explain the meaning of each. There are questions you have to answer in addition to the
tables and graphs. You will also be asked to explain similarities and differences. Your
explanations should include details and be written in paragraph form. How well you write is
a factor in demonstrating your understanding of the math involved in each scenario.
You will be assessed on the following:
o
Each of the 8 tables is worth 4 points. Data in tables should be accurate and
legible.
o
Each of the 7 graphs is worth 4 points. Graphs should be accurate and neat. Lines
should be drawn using a ruler.
o
The written answers are 30 points total. When asked to explain, you are expected
to write in complete sentences and highlight the vocabulary terms used.
o
The final conclusion you write at the end should be legible, in complete sentences
and detailed. This is worth 10 points.
You are expected to complete the project by the due date. Failure to do so will result in a
deduction of points for each day it is late. Also, you are expected to do your own work.
Copying another student’s work will result in a grade of 0 and an honor code violation. Your
scenario and your answers should be written in your own words and should be your own
ideas.
Name:______________________________
Date Assigned:__September 18, 2009______
Date Due: ___________________________
Time given to work on project:
The keypad on Sam’s cell phone is shown at right. As you can see,
there is a relationship between the letters and numbers. When
Sam writes a text message, he thinks of the letter in the
word he is typing and presses the correct numbered key.
1. Complete this table to show the relation from letter to number
Letter
A
B
C
Number
2
2
2
D
E
F
G
H
I
Z
2. What is the domain of this relation? ___________________________
3. What is the range of this relation?____________________________
4. Is the relation from letter to number a function? Explain using appropriate vocabulary
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5. If Sam writes the word “Hello,” what sequence of numbers does he press? _______________
After Sam presses the numbered keys, the microchip within his cell phone must decide what
letters to show on the screen. Consider the relation from number to letter.
6. What is the domain of this relation?___________________________________________
7. What is the range of this relation?____________________________________________
8. Is the relation from number to letter a function? Explain using appropriate vocabulary
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9. List the possible three-letter combinations the phone could show on the screen after Sam
presses 3 6 4.
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10. Sam’s phone uses predictive text messaging, which means that it “guesses” what word she
meant to type. Which three-letter word in problem 9 do you think the phone will guess? ________
Functions
Vacationers traveling outside the United States should be familiar with currency conversion rates
since currencies other than U.S. dollars are used in most other countries. As of September 29,
2006 one U.S. dollar was equivalent to 0.788 Euros. The equation used to figure the number of
Euros for any dollar amount is E  0.75D
1. Using the above equation complete the table showing the number of Euros from 0-$10
Dollars
Euros
0
1
2
10
2. Using the grid at the right, graph the
relationship for the exchange rate of dollars to
Euros
3. Determine if the relationship between dollars and Euros is a function? _______________
4. Explain your yes or no answer above using function vocabulary and citing 2 specific methods you
could have used in your determination.
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The number of teachers a school is allotted is based on a formula T 
the number of students.
s
where “s” represents
25
1. Complete the table
Students
Teachers
25
50
100
550
8
1000
32
2. Graph the relationship
3. Explain your rationale for whether the data should be represented as continuous or discrete
data.
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4. If Hopewell Middle school has an enrollment of 1,107 students, how many teachers would we be
allotted? ______________.
5. If we have 97 teachers how many students could we have? ____________
6. Can you represent this value as an inequality? _______________
Your parents send you to Home Depot to get 20 feet of fence to make a rectangular garden in your
back yard. The equation that represents all of the possible dimensions you can have for the length
“x” and the width “y” is y  10  x .
1. Complete the table for the possible lengths and widths
Length
(x)
Width
(y)
0
1
2
3
4
5
6
7
8
9
10
2. Create a graph from your table of values
3. Is this data discrete or continuous? _____________________________
4. This scenario is similar yet different than the previous two? In one paragraph detail the
similarities and differences in this relationship and the first two.
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1. The relationships on the previous 3 pages represent a specific type of function. Write a
paragraph explaining this type of function and how someone can identify this type of function
using an equation, table or graph.
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2. Using your knowledge of linear relationships write a brief scenario that would be modeled by a
linear function.
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3. Write the “rule” or equation that models your scenario ______________________________
4. Create a table for your scenario with at least 5 data points
5. Is your data discrete or continuous?________________________
6. Graph your data
Other Relationships
Scenario A
The dispersal pattern tolerances of a competition shotgun can be modeled by the equation
y  2x  1 where x is the distance in meters aimed left (-) or right (+) of the target and y
represents the distance down range away from the shooter.
1. Complete the table to represent this data
X
Y
-4
-3
-2
-1
0
1
2
3
4
5
2. Graph the relation
3. Is the above relation a function? Explain why or why not using the appropriate vocabulary.
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Scenario B
Think back to the trip you made to Home Depot to get the fencing for your garden. Your dad wants
to know what is the largest area you can enclose with the 20 feet of fencing.You tell pops that it
can be modeled by the equation y  10x  x 2 where “x” is the length of the garden in feet and “y”
is the area in square feet. Your dad asks you to show him using a table and graph.
1. Complete the table
Length
(X)
Area
(Y)
2.
0
1
2
3
4
5
6
7
8
9
10
Graph the relationship
3. Is the above relation a function? Explain why or why not using the appropriate vocabulary.
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Scenario C
The parabolic shape of the reflective inside of an automobile headlight can be modeled by the
equation x  y 2 .
1. Complete the table
X
y
-4
-3
-2
-1
0
1
2
3
4
2. Graph the relationship
3. Is the above relation a function? Explain why or why not using the appropriate vocabulary.
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Conclusions
The math teacher’s hypothesis about scenario A, B & C is that “each scenario has x and y
values therefore they all model linear functions”. Your job is to write no more than one page
giving details proving or disproving our hypothesis. Be sure to use complete sentences and
remember your grammar rules!
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