Let's examine the question carefully to determine the domain of Brenton's weekly pay function, [tex]$P(h)$[/tex], which is dependent on the number of hours he works, [tex]$h$[/tex].
First, we need to identify the possible range for the number of hours Brenton can work in a week. According to the problem, he can work from 0 hours to a maximum of 60 hours per week.
1. Minimum Hours:
- The smallest value for [tex]$h$[/tex] is 0. This means Brenton cannot work less than 0 hours in a week.
2. Maximum Hours:
- The largest value for [tex]$h$[/tex] is 60, as he is not permitted to work more than 60 hours in a week.
Given these constraints, the domain of [tex]$P(h)$[/tex], which represents the number of hours Brenton can work in a week, is the set of all possible hours he can work, ranging from 0 up to 60.
Among the provided options, the correct set that describes the domain of [tex]$P(h)$[/tex] is:
[tex]\[
\{ h \mid 0 \leq h \leq 60 \}
\][/tex]
Therefore, the correct answer from the given choices is:
[tex]\[
\{h \mid 0 \leq h \leq 60\}
\][/tex]
