A company produces a product using a machine that is prone to breaking down. The company's profit function is modeled by a rational function that is undefined at points where the machine breaks down. Which of the following statements about the profit function is true?

Core Concept

The primary reason the statement is true is that the company's profit function is modeled by a rational function that is undefined at points where the machine breaks down, which indicates that the function is continuous everywhere except at those points. This is a characteristic of rational functions with holes, not rational functions with vertical asymptotes. (B) is incorrect because the profit function is not always positive, as the machine's breakdowns can cause the function to be negative. (C) is incorrect because the function is not necessarily discontinuous at the points where the machine breaks down. (D) is incorrect because the function approaches a hole, not a vertical asymptote, when the machine breaks down.