Final answer:
The best domain for the function representing Jack's pay after school would be the range of hours he could realistically work, which is 0 to 6 hours. The correct option for Jack's work function domain is 0 ≤ x ≤ 6.
Step-by-step explanation:
The student is asking about the appropriate domain for a function that relates to the amount Jack, who works after school, earns each day through a set amount and an hourly wage. To determine the correct domain, we must consider the typical number of hours a student could reasonably work after school.
Given that a full-time working day typically consists of 8 hours, and knowing that this is after school hours, we can safely assume that Jack would not work more than this in a day. Therefore, a reasonable domain for the number of hours, x, that Jack could work after school would be between 0 and 8 hours. The domain 0 ≤ x ≤ 6 is the most appropriate for Jack's work function. This choice accounts for a part-time workday that accommodates after-school hours. The mention of the correct option in the final part of the answer is that the domain of the function Jack uses to determine his pay should be 0 ≤ x ≤ 6.