Final answer:
The correct function for the mail-order company's charging system is f(x) = 5 + 2x. The most accurate domain is the set of non-negative integers {0, 1, 2, 3, 4}, and the corresponding range for the total charges is the set {5, 7, 9, 11, 13}.
Step-by-step explanation:
The function to describe the mail-order company's charges is f(x) = 5 + 2x, where x is the number of items and f(x) is the total charge. The domain of the function must be the set of numbers that represent the possible quantity of items in an order, which here can only be from 0 to 4 items because the company charges for up to a maximum of 4 items only. Therefore, the domain is the set of non-negative integers {0, 1, 2, 3, 4}. As for the range, it consists of the total cost for these quantities of items. With each item adding $2 to the fixed charge of $5, the charges can only be $5, $7, $9, $11, and $13, corresponding to the number of items ordered. This means the range is the set {5, 7, 9, 11, 13}.
Considering these sets, the correct description of the function with its domain and range is answer option b): f(x) = 5 + 2x, Domain: x is a positive integer, Range: y is a positive real number. However, since the domain includes 0 (for orders with 0 items), it should actually be modified to state that the domain of x is a non-negative integer, thus making answer option a) the most accurate if we consider 0 a non-negative integer rather than a positive integer.