Question

vonda works between 30 and 32 hours per week at a hair salon. she pays a one time $250 chair rental fee, and earns $40 per hour that she works. the hours she works are rounded to the nearest quarter hour. the function $p(h) = 40h - 250$ represents vondas weekly pay as a function of hours worked. what is the practical domain of the function? all real numbers {30, 31, 32} $30 \leq h \leq 32$ {30, 30.25, 30.5, 30.75, 31, 31.25, 31.5, 31.75, 32}

Explanation:

Step1: Understand Domain & Practical Domain

The domain of a function is all possible input values (\(h\) here). Practical domain considers real - world constraints. Vonda works between 30 and 32 hours per week, and hours are rounded to the nearest quarter hour.

Step2: List Possible Hour Values

Quarter - hour increments mean we start at 30, then add 0.25 each time until we reach 32.

• Start with \(h = 30\)
• Then \(30+0.25 = 30.25\)
• \(30.25 + 0.25=30.5\)
• \(30.5+0.25 = 30.75\)
• \(30.75+0.25 = 31\)
• \(31 + 0.25=31.25\)
• \(31.25+0.25 = 31.5\)
• \(31.5+0.25 = 31.75\)
• \(31.75+0.25 = 32\)

So the practical domain is the set of these values: \(\{30, 30.25, 30.5, 30.75, 31, 31.25, 31.5, 31.75, 32\}\)

Let's eliminate other options:

• "all real numbers" is wrong because there are real - world constraints on hours worked.
• \(\{30, 31, 32\}\) is wrong because it doesn't consider the quarter - hour rounding (e.g., 30.25 is a valid number of hours worked).
• \(30\leq h\leq32\) is the domain of a continuous function, but here \(h\) is discrete (rounded to quarter hours), so this is incorrect.

Answer:

\(\{30, 30.25, 30.5, 30.75, 31, 31.25, 31.5, 31.75, 32\}\)