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The rate of customers who pass through the checkout stand at a grocery store depends on the time of day. Assume the rate follows the following piecewise-defined function, where represents the time of day (in hours) after 9:00 a.m. and is the number of customers served per hour. 

  1. Graph the function and state its domain and range.

    Your sketch should have three linear pieces.

    The domain is given by the piecewise function above.

    The range can be seen on the graph. What is the highest and lowest -value? Are there any holes or jumps on that interval?

  2. Is this function continuous?

    We know that the graph has a starting point so, it could only be continuous when .

    Be mindful of the conditions of continuity:

  3. Calculate the area under the curve for . What are the units of this area? What does this area represent?

    , where is some constant. The base is determined by the units on the -axis. The height is determined by the units on the -axis. Multiply.