Question

brenton’s weekly pay, p(h) , in dollars, is a function of the number of hours he works, h. he gets paid $20 per hour for the first 40 hours he works in a week. for any hours above that, he is paid overtime at $30 per hour. he is not permitted to work more than 60 hours in a week. which set describes the domain of p(h)? \\(\\{h|\\ 0 \leq h \leq 40\\}\\) \\(\\{h|\\ 0 \leq h \leq 60\\}\\) \\(\\{p(h)|\\ 0 \leq p(h) \leq 1,400\\}\\) \\(\\{p(h)|\\ 0 \leq p(h) \leq 1,800\\}\\)

Explanation:

Step1: Recall Domain Definition

Domain of a function \( P(h) \) is the set of all possible input values (\( h \), hours worked), not output (\( P(h) \), pay). So eliminate options with \( P(h) \) (third, fourth).

Step2: Determine Valid \( h \) Range

He can work 0 hours (minimum) up to 60 hours (maximum, as not permitted over 60). The first 40 hours are regular, but the upper limit is 60, so \( h \) is between 0 and 60, inclusive.

Answer:

\(\{h \mid 0 \leq h \leq 60\}\) (the second option)