Explanation:
f(x) is clearly the function that defines the hourly rates.
it is a set of 3 constants in 3 different areas of x values (the x values represent the number of hours).
f(x) = 0 for 0 < x <= 1
f(x) = 4 for 1 < x <= 6
f(x) = 2.5 for x > 6
obviously there are no negative values for hours.
the question was simply to write the textual list as mathematical function, which is separated in its "behavior" based on 3 different intervals of x (the hours involved).
I am not sure, if you need further explanation. please let me know.
as a summary :
as long as the number of hours is between 0 and 1 (the first hour is free, so, every fraction of part of the first hour is free) the hourly rate as functional result is $0.
as long as the number of hours (and any part of an hour in between) is between 1 and 6 hours, the hourly rate is $4.
and for his more than 6 the hourly rate is $2.50.
the tricky part is to find when to use "<" or ">", and when to use "<=". it is important to make sure that there is no "double definition" of f(x) for a value of x. therefore, we must make sure that the intervals are in one hand uninterrupted, but on the other hand not overlapping.
otherwise it would not be clear what to use in that case of x.