Question

A concession stand is selling popcorn. The money earned from popcorn sales can be represented by f(x)=1.5x , where f(x) represents the total amount of sales and x represents the number of bags sold. There are only 650 bags available. Write the domain and range of this situation.

Answer 1

Explanation:

"the amount of sales" is in my understanding the earned money.

y = f(x) = the money earned.

x = number of bags sold.

so, y = f(x) just tells us how much money is earned, when x bags are sold.

and f(x) = 1.5x (whatever monetary unit is used)

650 bags are available.

the domain tells us the valid values for x.

so, what are valid numbers of bags of popcorn sold ?

well, if all goes bad, they sell no popcorn at all = 0 bags.

if all goes great, they will sell all 650 bags. but not more, because they have not more than these 650 bags.

so, the valid x values (domain) are whole numbers with

0 <= x <= 650.

whole numbers, because the problem description sounds like they would not sell parts of bags.

the range tells us the valid/expected intervals or sets of values for y (= the functional result values).

so, what are the possible amounts of money they can earn ?

for x = 0, also y = 0 (per y = 1.5x).

this is, where y starts. it cannot be lower than 0.

and then y grows with x with the factor of 1.5.

and the maximum amount of earned money we get, when x reaches the maximum (= all 650 bags are sold).

x = 650, y = 1.5×650 = 975

so, for the range we have

0 <= y <= 975

and y are rational numbers (due to the 1.5 factor)