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    Algebra: Graphing Functions and Quadratic Equations

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    Practice Problems

    Directions: Show work to support your final result. Examples requiring mathematical work to support the result must be included, if final answer is correct but supporting work is missing. Examples that require a graph DO NOT need the graph submitted if you submit online.

    PART I: Practice Problems
    Use the function f(x) = for the following questions:

    a) Graph the function and state the window settings used so any minimum and/or maximum values can be viewed. You do not have to submit the graph online - only the window settings.

    b) Determine the relative minimum and relative maximum of the function using the calculator, rounded to hundredths.

    c) State the intervals over which the function is increasing and/or decreasing and explain using complete sentences what your answer means.

    1) Use the function f(x) = for the following:

    a) Sketch a graph and explain how you can tell by inspection of the graph that this function will have an inverse function.

    b) Determining the inverse function, f -1(x).

    c) Use composition of functions to demonstrate algebraically that the inverse function you determined in part b is actually correct. What should you get for the result of composition?

    d) Include a sketch of the inverse function on the same graph as f(x) and discuss the graphical relationship between the two graphs. If submitting online, describe what the graphs of the functions look like - be specific and identify any intercepts.

    2) a) Determine the equation of the line that passes through the point ( -2,7) and is PARALLEL to the line
    Write a brief explanation of your process.

    b) Determine the slope of the line through the points ( 5, -8) and ( -2, 6).

    3) Divide the following rational expression:

    4) Determine the y-intercept, vertex and any x-intercepts for the equation . You can
    do this graphically, algebraically, or both but you must explain how you are determining each answer.

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    Solution Summary

    Several problems requiring graphing of functions and quadratic equations are solved in detail.