Question

Consider the situation at the local farmer's market where teenagers have been selling pumpkins. They have sold most of their pumpkins for $650, and there are 5 pumpkins left for sale, priced at $25 per pumpkin. Write the function in notation, identify the independent and dependent variables, and create a reasonable domain and range for this situation.

A. Function Notation: (P(x) = 25x), Independent Variable: (x) (number of pumpkins), Dependent Variable: (P(x)) (total earnings), Domain: (x ≥ 0), Range: (P(x) ≥ 0)

B. Function Notation: (E(x) = 25x), Independent Variable: (E(x)) (total earnings), Dependent Variable: (x) (number of pumpkins), Domain: (E(x) ≥ 0), Range: (x ≥ 0)

C. Function Notation: (P(x) = 650 - 25x), Independent Variable: (x) (number of pumpkins), Dependent Variable: (P(x)) (total earnings), Domain: (0 ≤ x ≤ 5), Range: (0 ≤ P(x) ≤ 650)

D. Function Notation: (E(x) = 650 - 25x), Independent Variable: (E(x)) (total earnings), Dependent Variable: (x) (number of pumpkins), Domain: (0 ≤ E(x) ≤ 650), Range: (0 ≤ x ≤ 5)

Answer 1

The correct function for the pumpkin sale scenario would be E(x) = 650 + 25x, with x as the number of pumpkins sold and E(x) as the total earnings. The domain is 0 ≤ x ≤ 5 and the range is 650 ≤ E(x) ≤ 775.

Step-by-step explanation:

The correct representation of the situation with the pumpkins at the farmer's market involves recognizing that the independent variable is the number of pumpkins remaining, denoted by x, and the dependent variable is the total earnings from selling those pumpkins, which we can represent with a function like E(x). Since the teenagers already earned $650 and have 5 pumpkins left at $25 each, the correct function would be E(x) = 650 + 25x, which reflects the additional revenue earned from selling x pumpkins. The domain for this function is the number of pumpkins that can still be sold, so it ranges from 0 to 5, or 0 ≤ x ≤ 5. The range is the total earnings possible from selling the remaining pumpkins, which starts from $650 (if no more pumpkins are sold) and increases by $25 for each pumpkin sold, leading to a maximum of $650 + (5*$25) = $775, so 650 ≤ E(x) ≤ 775.