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Examine the function  graphed at right. Graph starts, with a closed circle, at the point, (negative 2, comma negative 1), rises to the point, (negative 1, comma 3), falls, passing through the point (0, comma 2), until the point (2, comma negative 1), then rises and stops, with a closed circle at the point (4, comma 3).

  1. Which -values have points on the graph? That is, describe the domain of .

    The domain includes and all the numbers between. .

  2. What are the possible outputs for ? That is, what is the range?

    The range includes , and all the numbers between. .

  3. Ricky thinks the range of is and . Is he correct? Why or why not?

    Is there a point on the graph for  or for

    He is not correct since he is missing all the values between his numbers.
    The curve is continuous, so the description needs to include all numbers, not just integers.

  4. Make a sketch of another function with the same domain and range as .

    There are many possibilities. Here is one example.

    Line segment from, (negative 2, comma 3), to (4, comma negative 1), with closed circles on each end.