Final answer:
The independent quantity in Bill's work scenario is the number of hours he works, and the dependent quantity is the income earned. The reasonable domain values for work hours are [0, 40], while the range for income is [$0, $480], based on a maximum of 40 hours of work at $12 per hour.
Step-by-step explanation:
In the given scenario involving Bill, the independent quantity is the number of hours Bill works each week, since it can vary depending on his choice, while the dependent quantity is the income earned, which is determined by the number of hours worked. To determine the reasonable domain and range for this situation, we consider the constraints provided: Bill earns $12 per hour and works at most 40 hours per week.
- The domain, representing the number of hours Bill can work, would range from 0 hours (if he chooses not to work) to a maximum of 40 hours.
- The range, representing his possible earnings, would start at $0 (if he does not work any hours) and could go up to a maximum of $480 ($12 per hour × 40 hours).
Therefore, the reasonable domain values are [0, 40] hours, and the corresponding range values for the weekly income would be [$0, $480].