A movie theater seats 500 people. For any particular show, the amount of money the theater makes is a function m(n) of the number of people, n, in attendance. If a ticket costs 2 dollars, find the domain and range of this function.

domain: ?≤ n ≤?
range: ?≤ m(n) ≤?

since the amount of money the theater makes is a function of the number of people, it is dependent on the number of people.

let n = number of people
let m = amount of money
since a ticket costs 2 dollars, the amount of money would be
m = 2n, or in function form,
m(n) = 2n

since the movie theater has capacity of 500, the domain (all possible values of n) would be:
0 ≤ n ≤ 500

the minimum amount of money the theater is 0 if n = 0 and maximum is 500*2 = 1000 if n = 500. therefore the range (all possible values of m) is:
0 ≤ m(n) ≤ 1000

hope this helps~ :)

Well, when it comes to movie theaters, let's remember the domain specifically refers to the valid values for the independent variable, in this case, the number of people, n, in attendance. Since the theater seats 500 people, the domain would be 0 ≤ n ≤ 500. We can't have negative people or more people than seats, right?

Now, for the range, m(n) represents the amount of money the theater makes for a particular show. Since each ticket costs 2 dollars, the theater will make 2 dollars for each person attending the show. So, if we let m(n) be the total money made, we can express it as m(n) = 2n.

Now, considering that the amount of money made will always be non-negative, given by the ticket price per person, the range would be 0 ≤ m(n). And, of course, the maximum amount the theater can make is when all the seats are filled, which would be 2 dollars times 500, so the maximum value of m(n) would be ≤ $1000.

Therefore, the domain is 0 ≤ n ≤ 500 and the range is 0 ≤ m(n) ≤ $1000.

The domain of the function m(n) represents the possible values for the number of people in attendance, which in this case is restricted by the seating capacity of the movie theater. Since the theater can seat 500 people, the domain would be:

Domain: 0 ≤ n ≤ 500

The range of the function m(n) represents the possible values for the amount of money made by the theater for a particular show. Since each ticket costs $2, the range would depend on the number of people in attendance. The minimum value for the range would be 0 (if no one attends the show), and the maximum value would be the total amount of money collected if all 500 seats are filled:

Range: 0 ≤ m(n) ≤ 1000.

To find the domain and range of the function, we need to consider the constraints and limitations given in the problem.

In this case, the movie theater seats 500 people, so the maximum number of people that can attend a show is 500. Therefore, the function is defined for values of n from 0 to 500, inclusive.

Domain: 0 ≤ n ≤ 500

The amount of money the theater makes, m(n), is determined by multiplying the number of people, n, by the cost of a ticket, which is $2. Therefore, the value of m(n) can range from 0 to the maximum revenue the theater can generate. The maximum revenue is obtained when the theater is at full capacity, which is 500 people.

Range: 0 ≤ m(n) ≤ 500 * $2 = $1000

Range: 0 ≤ m(n) ≤ $1000

So, the domain of the function is 0 ≤ n ≤ 500, and the range of the function is 0 ≤ m(n) ≤ $1000.