Consider the function f(x) = 1 / (x - 2). Which of the following statements is true about the behavior of the function f(x) as x approaches 2?

Core Concept

The primary reason this is true is that the function f(x) is not defined at x = 2, and the value of the function approaches ∞ as x approaches 2 from the left and negative ∞ as x approaches 2 from the right. Therefore, the function does not approach a limit as x approaches 2. Options A and D are incorrect because the function does not approach a limit; option C is incorrect because the function does not approach a maximum.