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 Vonda's weekly pay as a function of hours worked. What is the practical domain of the function?

Answer 1

{30, 30.25, 30.5, 30.75, 31, 31.25, 31.5, 31.75, 32} would be the correct answer.

I'm sure you searched for this answer elsewhere and got either {30, 30.25, 30.5, 30.75, 31, 31.25, 31.5, 31.75, 32} or {30, 31, 32}, while they are both similar answers and would probably both make sense, however, there is a keyword in the question that gives us the reasoning behind the correct answer.

Reread the question and pay attention to the bold text:

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.

Meaning that the hours (X values) that she works are rounded to the nearest quarter, which would eliminate {30, 31, 32}, because it does not include the quarters (.25 , .50 , .75)

Hopefully I helped.

: )

Answer 2

The practical domain of the function is [30,32].

Explanation:

The given function is

`p(h)=40h-250`

where, p(h) represents the Vonda's weekly pay as a function of hours worked.

She pays a one time $250 chair rental fee, and earns $40 per hour that she works.

Domain is the set of all possible inputs.

The possible domain of the given function is all real numbers but the number of hours can not be negative, therefore h>0.

It is given that Vonda works between 30 and 32 hours per week at a hair salon. So,

`30<h<32`

Therefore practical domain of the function is [30,32].