To determine $f(2)$ using the graph provided, let's analyze the point where $x = 2$.

Step-by-Step Solution:

1. Locate $x = 2$ on the graph: Find the point on the graph corresponding to $x = 2$.

2. Identify $f(2)$: Look at the value of $y$ (i.e., $f(x)$) at $x = 2$.

   • The graph shows a filled dot at the point $(2, 3)$, which indicates that the value of the function $f(2) = 3$.

3. Final Answer: Since $f(2)$ corresponds to the $y$-value of the point $(2, 3)$, we conclude that $f(2) = 3$.

Explanation:

The correct answer is 3, as the filled dot at $(2, 3)$ represents the actual value of the function at $x = 2$.

Would you like more details on this topic or have any further questions?

Here are five related questions for you to explore:

1. How do you determine if a limit exists at a point using a graph?
2. What is the difference between a limit and the actual value of a function at a point?
3. How do you find one-sided limits on a graph?
4. What happens if a function has a discontinuity at a point?
5. Can a function have different left-hand and right-hand limits at the same point?

Tip: When determining function values from a graph, always pay attention to whether the point is filled (indicating the function's value) or open (indicating that the function does not take that value there).