The reasonable domain for the function that represents the cost of renting a car from this company depends on the number of hours you can rent the car and the way partial hours are billed.
- The maximum number of hours you can rent the car is 8 hours.
- Since the company charges for any part of an hour by rounding it up to the next hour, the minimum time you can rent the car is 1 hour (even if you only need it for a few minutes).
Thus, the reasonable domain, in hours, for the number of hours \( h \) that you can rent the car is:
\[ h \in [1, 8] \]
This means that \( h \) can take any value from 1 to 8, inclusive. In set notation, this can be expressed as:
\[ { h | 1 \leq h \leq 8 } \]