# Math Help - Function word problem.

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 $f(x)= 45x + 55$ 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 $0 \leq x \leq12$
Range $0\leq x \leq 595$

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 $f(x) = 595$ 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 $55\leq x \leq 595$