Question

The graph of the revenue function f(x) = –0.07x2 + 3.5x is used to determine revenue in hundreds of thousands of dollars, where revenue depends on the number of thousands of items sold, x.

How do the mathematical domain and reasonable domain compare?

A. mathematical: –∞ < x < ∞ reasonable: 0 ≤ x ≤ 25
B. mathematical: –∞ < x < ∞ reasonable: 0 ≤ x ≤ 50
C. mathematical: 0 < x < ∞ reasonable: 0 ≤ x ≤ 25
D. mathematical: 0 < x < ∞ reasonable: 0 ≤ x ≤ 50

Answer 1

To compare the mathematical domain and reasonable domain, we need to understand what they mean.

The mathematical domain is the set of all possible values of the independent variable, which is x in this case. The reasonable domain is the set of all possible values of the independent variable that make sense for the given situation

For this function, f(x) = –0.07x2 + 3.5x, the mathematical domain is –∞ < x < ∞, because there is no restriction on the values of x that can be plugged into the function.

However, the reasonable domain depends on the context of the problem. Since x represents the number of thousands of items sold, it does not make sense for x to be negative or too large. Looking at the graph, we can see that the function has a maximum value at x = 25, and then it becomes negative after that point. Therefore, a reasonable domain for this function is 0 ≤ x ≤ 25.

So, the correct answer is A. mathematical: –∞ < x < ∞ reasonable: 0 ≤ x ≤ 25

Explanation: