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    Comparing Relations and Functions

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    1. In the real world, what might be a situation where it is preferable for the data to form a relation but not a function?
    2. There is a formula that converts temperature in degrees Celsius to temperature in degrees Fahrenheit. You are given the following data points:
    Fahrenheit Celsius
    Freezing point of water 32 0
    Boiling point of water 212 100
    1. Find the linear equation that expresses temperature in degrees Fahrenheit as a function of temperature in degrees Celsius.
    2. Find the linear equation that expresses temperature in degrees Celsius as a function of temperature in degrees Fahrenheit.
    3. How do the graphs of these two functions differ?
    Do not just list the functions. You must show all of the steps you used to derive the functions.
    You have been invited to present statistical information at a conference. To prepare, you must perform the following tasks:
    1. The following data was retrieved from www.cdc.gov. It represents the number of deaths in the United States due to heart Disease and cancer in each of the years; 1985, 1990, 1995, and 2002.
    Disease 1985 1990 1995 2002
    Heart Disease 771169 720058 737563 696,947
    Cancer 461563 505322 538445 557,271
    a. Plot this data for each disease as points in a rectangular coordinate system.
    b. Using a smooth line, connect your data points for each disease.
    c. On a separate graph, plot only the years 1985 and 2002 and connect the points with a straight line.
    d. Calculate the slope of each line.
    e. Write the equation of each line in the slope-intercept form.
    f. Using the equations of each line, make a reasonable prediction as to the number of deaths we might expect in 2005 due to each of these medical conditions.

    3. Please include a response to this two part follow-up question with your submission.
    a. Can the graphs that you constructed be classified as functions? Explain.
    b. Why is it reasonable that negative numbers are excluded from both the domain and the range of each of the disease graphs? What would the real-world implications be if these numbers were actually part of the domain and/or range?

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    Solution Summary

    Relations and functions are investigated. The solution is detailed and well presented.