The graph of the function f(x) approaches the value 2 as x gets arbitrarily close to -1, but never touches it. Which of the following statements is true?

Core Concept

The primary reason this is true is that the limit represents the value that the function approaches as x gets arbitrarily close to the point, even if it doesn't touch it. The limit exists because the function approaches a single value as x approaches -1. Options B and D are incorrect because the limit exists; option C is incorrect because the function does not actually reach the value 2 at x = -1.