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Math Help - Function word problem.

  1. #1
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    Function word problem.

    Hi

    I am having some trouble with the following :

    A real estate agent determines the costs of maintaining and hiring a hall by charging a flat fee for maintenance of $55 then an hourly fee of $45 an hour. The maximum charge for a full days use is $595.

    Write a mathematical expression to generate to cost of hiring the hall:

    The best I can come up with is f(x)= 45x + 55

    But this does not faction in the $595 maximum however the next question is, what is the domain and range of the function assuming agents allow parts of an hour to be considered.

    would this mean the:

    Domain 0            $\leq$ x           $\leq$12
    Range 0$\leq$ x $\leq$ 595
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  2. #2
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    e^(i*pi)'s Avatar
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    f(x) is fine

    As you say at the end the $595 is upper limit of f(x) which is of course the maximum value of the range and since money isn't negative then 0 is the minimum value making your range fine.

    The domain (number of hours) is minimum 0 and maximum for the value of x such that f(x) = 595 which is 12

    In other words you're correct
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  3. #3
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    I was slightly incorrect I think, I'm sure the range should actually be:

    Range 55$\leq$ x $\leq$ 595
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