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Sketch a graph of the piecewise-defined function .   

  1. State the domain and range of .

    Consider the domain and range of each piece separately . Then combine.
    Domain: Both and have a domain of all real numbers.
    Range: on has a range of and on has a range of .

  2. Is continuous at ? Explain.

    Later in this course we will learn a formal definition of continuity. For now, think about what continuous means to you. Now look at the graph at . Make a conclusion and justify.

  3. Is continuous for all values of ?

    Consider other values of , other than . Is the function continuous at these point? Is there anywhere where the function will not be continuous?

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Click the link at right for the full version of the eTool: Calc 1-24 HW eTool