Question

f(15)= - 45, meaning when the width of the rectangular area is 15 ft, the area would be - 45 ft². this interpretation does not make sense in the context of the problem. based on the observations above, it is clear that an appropriate domain for the function is all real numbers non - negative real numbers real numbers in a<x<b integers whole numbers (0, 1, 2, ...) positive integers (1, 2, 3, ...) integers in a<x<b

Explanation:

Step1: Analyze the context

The function represents the area of a rectangle. Area cannot be negative in a real - world geometric context. Width is a physical quantity related to the rectangle.

Step2: Recall domain rules

In the context of geometric measurements like width, it must be non - negative. Real numbers include negative numbers, which are not valid for width. Integers may not cover all possible values of width (e.g., width could be a non - integer like 1.5). Whole numbers start from 0, but a width of 0 would mean no rectangle. Positive integers also exclude non - integer values for width. The most appropriate set for the width (input of the function) is non - negative real numbers as it includes 0 and all positive real values which can represent possible widths of a rectangle.

Answer:

non - negative real numbers