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    Polynomial, rational, exponential and logarithmic functions.

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    Your manager is very please with your presentations and being able to show your calculations in a detailed fashion. He has asked that you help him prepare for the upcoming company summit. Before you get together, he has asked that you give him a little review on polynomial functions and how you would apply them to everyday use. You have thought about the different methods in showing him the different methods used in calculating the functions and have drawn up an action plan.

    To exercise your skills, you are to perform the following using different tools available to you (e.g. Excel spreadsheet, graphing calculator, etc.) and write and explanation on your findings:

    The graph of: f(x)= 0
    The graph of: f(x) = a0 , where a0 ≠ 0
    The graph of: f(x) = a0 + a1x , where a1 ≠ 0

    For each of the three above:

    What does the graph look like -- describe the x placement
    What is the graph function called?
    Give an example of a number you could place in for the variable x, and describe the shift from the original graph. Remember to note what your value you are calculating for the variable x.
    Your complete assignment must include both your answers and your calculations.

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    Solution Preview

    To exercise your skills, you are to perform the following using different tools available to you (e.g. Excel spreadsheet, graphing calculator, etc.) and write an explanation on your findings:

    When graphing a function f(x), you're drawing a picture of the infinite number of points (x, y) where x is any number, and y is the value of f(x) that you get after plugging the value for x into the function.

    To make the graphs of f(x) below, I chose several values of x, found the corresponding f(x) values, and used Excel to graph them. You could use this method, or you could graph them by hand, or use a graphing calculator.

    The graph of: f(x) = 0

    Here are some values for x and the corresponding values for f(x). f(x) = 0 for all values of x.

    x f(x)
    -3 0
    -2 0
    -1 0
    0 0
    1 0
    2 0
    3 0

    When you graph f(x) = 0, the ...

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