A machine's malfunction causes a metal rod to be inserted into a piece of clay, creating a hole. Which of the following statements about the function that models the volume of the hole is true?

Core Concept

The primary reason the statement is true is that the function models the volume of the hole, and the point of insertion is a discontinuity in the function because it represents a change in the volume of the hole. (A) is incorrect because the function is not continuous everywhere except at the point of insertion. (C) is incorrect because a discontinuity represents a sudden change in the function, whereas a hole in the clay represents a gradual change. (D) is incorrect because a horizontal asymptote represents a limit as x approaches ∞, not as x approaches a point of discontinuity.