ࡱ> VXUe%` Dbjbj"x"x 4@@<bbbbbbbv^M^M^M^MdMvNOOOOOOO5777777$jhҜ[baQOOaQaQ[bbOOpTTTaQ*bObO5TaQ5TTNbbύON Q8^MR00ˋnySn`ύύnbOLO6TP,.P3OOO[[TOOOaQaQaQaQvvv0:5$vvv:5vvvbbbbbb 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: Each of the 8 tables is worth 4 points. Data in tables should be accurate and legible. Each of the 7 graphs is worth 4 points. Graphs should be accurate and neat. Lines should be drawn using a ruler. 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. 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 students 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 Sams 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 LetterABCDEFGHIZNumber222 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 __________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ 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 __________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ 9. List the possible three-letter combinations the phone could show on the screen after Sam presses 3 6 4. ____________________________________________________________________________________________________________________________________________________ 10. Sams 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  EMBED Equation.3  Using the above equation complete the table showing the number of Euros from 0-$10 Dollars01210Euros 2. Using the grid at the right, graph the relationship for the exchange rate of dollars to Euros INCLUDEPICTURE "../../../../../../../../../../Program%20Files/TI%20Education/TI%20InterActive!/TIIimagefile9064.gif" \* MERGEFORMAT  Determine if the relationship between dollars and Euros is a function? _______________ Explain your yes or no answer above using function vocabulary and citing 2 specific methods you could have used in your determination. ____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ The number of teachers a school is allotted is based on a formula  EMBED Equation.3  where s represents the number of students. Complete the table Students25501005501000Teachers832 2. Graph the relationship  INCLUDEPICTURE "../../../../../../../../../../Program%20Files/TI%20Education/TI%20InterActive!/TIIimagefile15451.gif" \* MERGEFORMAT  Explain your rationale for whether the data should be represented as continuous or discrete data. _________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ If Hopewell Middle school has an enrollment of 1,107 students, how many teachers would we be allotted? ______________. If we have 97 teachers how many students could we have? ____________ 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  EMBED Equation.3 . Complete the table for the possible lengths and widths Length (x)012345678910Width (y) 2. Create a graph from your table of values INCLUDEPICTURE "../../../../../../../../../../Program%20Files/TI%20Education/TI%20InterActive!/TIIimagefile14194.gif" \* MERGEFORMAT   Is this data discrete or continuous? _____________________________ 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. ____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ 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. ____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ Using your knowledge of linear relationships write a brief scenario that would be modeled by a linear function. __________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ Write the rule or equation that models your scenario ______________________________ Create a table for your scenario with at least 5 data points  Is your data discrete or continuous?________________________ 6. Graph your data INCLUDEPICTURE "../../../../../../../../../../Program%20Files/TI%20Education/TI%20InterActive!/TIIimagefile22312.gif" \* MERGEFORMAT  Other Relationships Scenario A The dispersal pattern tolerances of a competition shotgun can be modeled by the equation  EMBED Equation.3  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. Complete the table to represent this data X-4-3-2-1012345Y 2. Graph the relation INCLUDEPICTURE "../../../../../../../../../../Program%20Files/TI%20Education/TI%20InterActive!/TIIimagefile26071.gif" \* MERGEFORMAT  3. Is the above relation a function? Explain why or why not using the appropriate vocabulary. ________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ 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  EMBED Equation.3  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. Complete the table Length (X)012345678910Area (Y) 2. Graph the relationship INCLUDEPICTURE "../../../../../../../../../../Program%20Files/TI%20Education/TI%20InterActive!/TIIimagefile31525.gif" \* MERGEFORMAT  3. Is the above relation a function? Explain why or why not using the appropriate vocabulary. ________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ Scenario C The parabolic shape of the reflective inside of an automobile headlight can be modeled by the equation  EMBED Equation.3 . Complete the table Xy-4-3-2-101234 2. Graph the relationship INCLUDEPICTURE "../../../../../../../../../../Program%20Files/TI%20Education/TI%20InterActive!/TIIimagefile621.gif" \* MERGEFORMAT   3. Is the above relation a function? Explain why or why not using the appropriate vocabulary. ________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ Conclusions The math teachers 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. 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