Question

Bonnie will buy up to 200 paper cups for a party. She found a store that sells paper cups in packages of 25. The function c(p) = 25p represents the number of cups Bonnie would have if she bought p packages of cups from this store.
(a) What are the theoretical domain and range of function c?

(b) What are the practical domain and range of function c?

Answer 1

I need only part b

Answer 2

What did you get for part A?

Answer 3

All the set of real numbers except for 0

Answer 4

Very good, except even zero would be included in the domain and range, since the function is defined for zero. ie doesn't have a divide by zero or things like that

SO practically what would the range be? It's not like I will go the store and sell them packages of cups when I actually need cups.

Answer 5

all real numbers between 0 and 200

Answer 6

Why zero? That wouldn't be practical, at least to me, to drive to the store with the intent of buying nothing. Although, many times I have driven to a store and ended up buy nothing. So many zero is okay, but I don't think so.

As for the upper end, 200 might be the practical upper choice. If you assume you need at least 200 cups and maybe you buy 200 individually wrapped cups. 200 could be very practical. With that reasoning, you might go to the store and find 1 package with 200 cups.

So I really don't know if this is correct, I could be totally off base, but practically is too vague for me to figure out. So if I had to guess I would say practically the domain could be from 1 to 200, even though it could go to infinity. I don't think you could practically buy an infinity number of packages of cups. Unless you had an infinite amount of money.