The graph provided shows the function $f(x)$, and the question relates to its properties at $x = 2$. Let's analyze the options based on the graph:

• Is $f(2)$ defined?
  From the graph, at $x = 2$, the function has a point (a filled circle) at $(2, 3)$. This indicates that $f(2)$ is defined and equals 3.

• Does the limit $\lim_{x \to 2} f(x)$ exist?
  The left and right-hand limits as $x$ approaches 2 are both equal to 3 (since the graph approaches the same value from both sides), so the limit exists.

• Is $\lim_{x \to 2} f(x) = f(2)$?
  Since the limit as $x$ approaches 2 equals 3, and the function value at $x = 2$ is also 3, we can confirm that $\lim_{x \to 2} f(x) = f(2)$.

• Is the function continuous at $x = 2$?
  Since the limit exists and equals $f(2)$, and $f(2)$ is defined, the function is continuous at $x = 2$.

Thus, based on the graph:

• The correct selections would be:
  • $f(2)$ is defined.
  • $\lim_{x \to 2} f(x)$ exists.
  • $\lim_{x \to 2} f(x) = f(2)$.
  • The function is continuous at $x = 2$.

Would you like further details or clarifications about this?

Here are some related questions to expand on this:

1. How do you determine if a function is continuous at a point from a graph?
2. What is the difference between a filled and open circle on a graph?
3. How can you compute limits from a graph?
4. What are the three conditions for continuity at a point?
5. What are some examples of functions that are not continuous at a point?

Tip: When checking for continuity at a point, always verify the following: the function is defined at the point, the limit exists at that point, and the function's value equals the limit at that point.