Question

A movie theater seats people. For any particular show, the amount of money the theater makes is a function, , of the number of people, , in attendance. If a ticket costs , find the domain and range of this function. The domain of is the set of integer multiples of

Answer 1

The domain of the function is the set of integer multiples of the number of people in attendance, and the range is the set of possible amounts of money the theater can make.

Step-by-step explanation:

The domain of a function represents the set of all possible input values, while the range represents the set of all possible output values. In this case, the domain is the set of integer multiples of the number of people in attendance, and the range is the set of possible amounts of money the theater can make.

Let's say the number of people in attendance is represented by the variable x. Since a ticket costs Price, the function can be written as: Revenue(x) = x * Price.

Therefore, the domain is the set of integer multiples of x, which can be represented as: Domain = x = nk, n is an integer.

The range is the set of possible revenue values, which is determined by the combination of ticket price and the number of people in attendance. The range depends on the specific values of Price and x.

Answer 2

`n \in [0,1,2,....200] , n \in [0,200]` because the maximum capacity is 200 people

And based on the values for the domain we can define the range like this:

`A \in [0,4,8,12,16,.......,800]`

Step-by-step explanation:

Assuming the following problem :"A movie theatre seats 200 people. For any particular show, the amount of money the theatre makes isa function of the number of people, n, that attend. If a ticket costs $4, state the domain and range of this function"

For this case based on the info the function would be:

`A= 4n`

Where A represent the amount of money collected and n the number of people that attend.

As we can see the domain on this case would be:

`n \in [0,1,2,....200]` because the maximum capacity is 200 people

And based on the values for the domain we can define the range like this:

`A \in [0,4,8,12,16,.......,800]`