Question

Please help. I WILL FAN AND MEDAL

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 school wants to make a play, and they paid $1,200
Now they are in debt of $1,200 so in order to get money, they charge the students $4 for watching the play.
Only 500 seats are available, so max is 500 people.
So a profit, is the amount of money you made ABOVE what you paid, which is $1,200
sooooo

If we model the number of students as x:
f(x) = 4x <--- The money you gain.

And since we want to know the profit, then:
f(x) = 4x - 1200 <-- The money you made minus the money you paid.

Since x can only go up to 500, then we plug 500 in:
f(500) = 4(500) - 1200
This will be the maximum. Can you figure that out?

Now for the minimum, we can assume that 0 people showed up. :(
We'd plug 0 in:
f(0) = 4(0) - 1200
This will be the minimum. I think you can figure this one out.

So the domain will be Minimum to Maximum.

Answer 2

I'm confused with answers A and B?

Answer 3

@mhchen

Answer 4

Um,,, there is no A or B?

Answer 5

It's just the minimum amount of money you'll make in total, to the maximum amount of money you'll make in total.

Answer 6

No, the answer choices. There is for so I associated them with A,B,C,D. I think if it's C. Or the third choice.

Answer 7

It is*

Answer 8

@mhchen

Answer 9

Okay.........soo um forget everything I just said :) (Sorry, I was finding the range)

Answer 10

All you had to know was that it holds 500 people. So it's 0-500.

Answer 11

That's like the input, which is the domain, and it has to be integers because you can't have like 1/5 of a person sitting down with their heads cut off or something,

Answer 12

So it's all integers from 0-500. Sorry I kinda calculated the range instead. :\

Answer 13

@brooke..help00
First in a function, we need to know what is the
- independent variable
- dependent variable
A function is like a machine that spits out numbers (the dependent variable) when you feed in numbers (the dependent variable).

We call the output numbers dependent variable because we cannot control any number we put in because it (\(depends\) on the function and the number we put in.

Similarly, we can put in any number we want into the machine, that explains the term \(independent~variable\), but subject to one condition, it must be within limitations called the \(domain\). I.e. we can only feed numbers within the domain.

Similarly, the set of all possible numbers coming out of the machine is called the \(range\).

Example:
A parking garage charges by the number of hours parked, as follows:
from 1-30 minutes: $5
31 to 60 minutes: $10
60 to 120 minutes: $y=(x-60)/6+10
121 to 24 hours: $30
after 24 hours: car will be towed.
Here : input is time parked, output is the parking fee.
So the domain is all possible time a person can charge, namely 1 min to 24 hours.
The range is all possible charges, namely, $5, $10 to $30.