Question

A school puts on a play. The play costs $1,200 in expenses. The students charge $4.00 for tickets. There will be one performance of the play in an auditorium that seats 500 people. What is the domain of the function that shows the profit as a function of the number of tickets sold?

The domain is all real numbers from negative 1,200 to positive 2,000
The domain is all integers from negative 1,200 to positive 2,000.
The domain is the integers from 0 to 500.
The domain is all real numbers from 0 to 500.

Answer 1

The domain is the integers from 0 to 500 because the tickets will be purchased by people and because the seats are limited to 500.  Also, you cannot sell a negative amount of tickets.

Answer 2

The domain is the integers from 0 to 500.

Explanation:

It is given in the problem "...function that shows the profit as a function of the number of tickets sold"

Here, the independent variable is the number of tickets

Since the auditorium has 500 seats, we can sell a maximum of 500 tickets and a minimum of 0 tickets. There cannot be fractional person, so the domain of the function is all integers from 0 to 500.