Question

brentons 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)? \bigcirc \\{h\mid 0 \leq h \leq 40\\} \bigcirc \\{h\mid 0 \leq h \leq 60\\} \bigcirc \\{p(h)\mid 0 \leq p(h) \leq 1,400\\} \bigcirc \\{p(h)\mid 0 \leq p(h) \leq 1,800\\}

Explanation:

Step1: Identify domain definition

The domain of a function is the set of possible input values. Here, the input is \( h \) (hours worked).

Step2: Determine valid h range

Brenton can work 0 hours (minimum) up to 60 hours (maximum, as he can't work more than 60). So \( 0 \leq h \leq 60 \).

Step3: Match with options

Option B describes this range for \( h \). Options C/D are about the output \( P(h) \), not the domain. Option A only covers up to 40 hours, missing overtime hours. Thus B is correct.

Answer:

B. {h | 0 ≤ h ≤ 60}