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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).

Use the graph of f shown to find the indicated limit or function value. If the limit does not exist, explain why. What is f(2)?

Learn how to determine the function value f(2) using a graph. Understand the key concepts of limits, function values, and graph interpretation. Suitable for students in Grades 10-12.

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