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    Functions, relations, and linear equations

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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?

    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

    2. Find the linear equation that expresses temperature in degrees Fahrenheit as a function of temperature in degrees Celsius.

    3. Find the linear equation that expresses temperature in degrees Celsius as a function of temperature in degrees Fahrenheit.

    4. How do the graphs of these two functions differ?

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    First of all, let us define a function: A function is a relation where no x -value apperas more than once (with different y-values).

    A one-to-one function is a function whereeach x -value corresponds to only one y-value.
    A regular function can occur when one y-value correspond to 2 x-values.

    There is an easy way to remember this:

    Let us say that the data represented by x values is kids (John, Rick, Bill, Tom)
    And the one that is represented by y-values is mothers ( Mary, Sue, Anne)
    (Domain) (Range)
    Kids Mothers
    John Mary

    Rick Sue

    Bill Anne

    Tom Lina

    As you can see, John CANNOT have 2 mothers, but Anne CAN have 2 kids.

    Of course, a One-to-One function occurs when Each Mother ...