1. ## 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 $595. Write a mathematical expression to generate to cost of hiring the hall: The best I can come up with is$\displaystyle 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 $\displaystyle 0$\leq$x$\leq$12$
Range $\displaystyle 0$\leq$x$\leq$595$

2. f(x) is fine

As you say at the end the $595 is upper limit of f(x) which is of course the maximum value of the range and since money isn't negative then 0 is the minimum value making your range fine. The domain (number of hours) is minimum 0 and maximum for the value of x such that$\displaystyle f(x) = 595$which is 12 In other words you're correct 3. I was slightly incorrect I think, I'm sure the range should actually be: Range$\displaystyle 55$\leq$ x $\leq$ 595\$