The problem presented asks for the limit of $f(x)$ as $x$ approaches 3, using the graph of the function $f$. Specifically, it wants:

$\lim_{x \to 3} f(x)$

Analyzing the Graph:

Looking at the graph, we observe the behavior of the function near $x = 3$:

• From the left-hand side ($x \to 3^-$), the graph approaches a value of 2.
• From the right-hand side ($x \to 3^+$), the graph also approaches a value of 2.

Since both the left-hand limit and the right-hand limit as $x \to 3$ are equal to 2, the limit exists and is equal to 2.

Thus, the correct answer is: $\boxed{2}$

Would you like more details or have any other questions about this solution?

Here are 5 related questions:

1. What is the definition of a limit?
2. How do you determine if a limit exists based on a graph?
3. What is the difference between a one-sided and two-sided limit?
4. How can discontinuities affect the existence of limits?
5. What is the meaning of a limit approaching infinity?

Tip: When analyzing limits graphically, always check the behavior of the function from both the left and right sides near the point of interest.