Question

Which of the following is a reasonable domain for the situation represented by the function m(c) = 10 - 2c, where m is the amount of money Caleb has left and c is the number of pieces of candy he buys?

A) x
B) x = 0, 1, 2, 3, 4, 5
C) x
D) 0 ≤ x ≤ 10

Answer 1

The reasonable domain for the function representing Caleb's money after buying c pieces of candy is all integers from 0 to 5, inclusive, which relates to option C) 0 ≤ x ≤ 5.

Step-by-step explanation:

The function m(c) = 10 - 2c represents the amount of money Caleb has left after buying c pieces of candy. To determine the reasonable domain for the number of pieces of candy Caleb can buy, we need to consider the physical constraints of the situation. Since Caleb cannot buy a negative number of candies, and assuming he cannot buy fractional pieces of candy, the domain must consist of all non-negative integers. We also know that c must be such that m(c) >= 0, because Caleb cannot have less than $0. This gives us an equation to solve for the maximum number of candies c. Solving for the inequality 10 - 2c ≥ 0, we get c ≤ 5. Hence, the domain is the set of all integers from 0 to 5, inclusive, which is option C) x .