Question

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) ≤?

Answer 1

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~ :)