Relations and Functions Project - 8th Grade Math



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 |[pic] |

|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 |

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 [pic] where “s” represents the number of students.

1. Complete the table

|Students |25 |50 |100 | |550 | |1000 |

|Teachers | | | |8 | |32 | |

|2. Graph the relationship |[pic] |

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 [pic].

1. Complete the table for the possible lengths and widths

|Length (x) |0 |

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

| | |

Other Relationships

Scenario A

The dispersal pattern tolerances of a competition shotgun can be modeled by the equation [pic] 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 |-4 |

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 [pic] 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) |0 |

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 [pic].

1. Complete the table

|X | |

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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