A movie theater seats 400 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
s400
The domain of the function, m(n), represents all the possible values for the number of people, n, in attendance. In this case, the domain is limited by the capacity of the movie theater, which is 400 people. Therefore, the domain of the function is 0 ≤ n ≤ 400.
The range of the function, m(n), represents all the possible values for the amount of money the theater makes. Since each person pays $2 for a ticket, the amount of money made is directly proportional to the number of people in attendance. Therefore, the range of the function is all non-negative multiples of $2. In other words, the range of the function is 0 ≤ m(n) ≤ $800.
To summarize:
Domain: 0 ≤ n ≤ 400
Range: 0 ≤ m(n) ≤ $800
To find the domain and range of the function m(n), we need to consider the limitations and possible values for the number of people in attendance.
Domain: The domain refers to the possible input values for the function. In this case, the number of people, n, cannot exceed the seating capacity of the theater, which is 400. Additionally, the number of people cannot be negative or zero, as it does not make sense to have negative or no attendees. Therefore, the domain of this function would be:
Domain: {n | 0 < n ≤ 400}
Range: The range refers to the possible output values of the function. In this case, the function is defined as the amount of money the theater makes, which is dependent on the number of people attending the show. Since the ticket cost is $2 per person, the range of the function would be all possible values for the amount of money made.
Range: {m | m = 2n, 0 ≤ m}
In summary:
Domain: {n | 0 < n ≤ 400}
Range: {m | m = 2n, 0 ≤ m}