Let's re-evaluate the graph to determine the correct value of \( f(3) \).

### Re-evaluation of \( f(3) \)

From the graph:
- At \( x = 3 \), the function \( f \) has an open circle at \( y = 4 \) and a filled circle at \( y = 2 \).
- The filled circle represents the actual value of the function at that point, while the open circle indicates a point that the function does not actually attain.

Therefore, \( f(3) = 4 \).

So the correct answers should be:

(a) \(\lim_{{x \to 0}} f(x) = 3\) ✓
(b) \(\lim_{{x \to 3^-}} f(x) = 4\) ✓
(c) \(\lim_{{x \to 3^+}} f(x) = 2\) ✓
(d) \(\lim_{{x \to 3}} f(x) = \text{none}\) ✓
(e) \(f(3) = 4\) ✓

My earlier analysis was incorrect. \( f(3) = 4 \) is indeed correct.

Do you have any questions or need further details?

Here are five questions you might ask next:

1. How can you identify the value of a function at a specific point from a graph with both open and closed circles?
2. What are the different types of discontinuities in a function?
3. How do you evaluate limits at points of discontinuity?
4. What is the difference between a limit approaching from the left and from the right?
5. How can you graphically determine if a limit does not exist?

**Tip:** When evaluating a function's value at a specific point from a graph, always look for the filled circle (indicating the actual function value) and distinguish it from open circles (indicating points that are not included in the function's value at that point).

Explore how to evaluate a function's value at a specific point using graphical analysis. Learn about limits and function continuity with examples. Suitable for high school students and anyone interested in calculus concepts.

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