A company's profit function is modeled by a function that is continuous everywhere except at a point where the company's machine breaks down. Which of the following statements about the function is true?

Core Concept

The primary reason the statement is true is that the company's profit function is modeled by a function that is continuous everywhere except at a point where the company's machine breaks down, which indicates that the function is discontinuous at that point. This is a characteristic of rational functions with holes, not rational functions with vertical asymptotes. (A) is incorrect because the function reaches its maximum value at the point where the machine breaks down. (C) is incorrect because a horizontal asymptote represents a limit as x approaches ∞, not as x approaches a point of discontinuity. (D) is incorrect because a vertical asymptote represents a point of discontinuity, but it is not necessarily the point where the machine breaks down.