Explain what is meant by the equation lim x → 2 f(x) = 3. The values of f(x) can be made as close to 2 as we like by taking x sufficiently close to 3. The values of f(x) can be made as close to 3 as we like by taking x sufficiently close to 2. f(x) = 3 for all values of x. If |x1 − 2| < |x2 − 2|, then |f(x1) − 3|≤ |f(x2) − 3|. If |x1 − 2| < |x2 − 2|, then |f(x1) − 3| < |f(x2) − 3|. Is it possible for this statement to be true and yet f(2) = 4? Explain. Yes, the graph could have a hole at (2, 3) and be defined such that f(2) = 4. Yes, the graph could have a vertical asymptote at x = 2 and be defined such that f(2) = 4. No, if f(2) = 4, then lim x→2 f(x) = 4. No, if lim x→2 f(x) = 3, then f(2) = 3.