A function f(x) is defined as f(x) = (x² - 4)/(x + 2) for x ≠ -2. Which of the following values of f(x) best describes the behavior of the function as x approaches -2?

Core Concept

To find the behavior of the function f(x) = (x² - 4)/(x + 2) as x approaches -2, we can simplify the expression by factoring the numerator: f(x) = (x - 2)(x + 2)/(x + 2). Canceling the (x + 2) term, we get f(x) = x - 2. As x approaches -2, f(x) approaches positive ∞. The correct answer is B) f(x) approaches positive ∞. Options A, C, and D are incorrect because they do not accurately describe the behavior of the function as x approaches -2.