https://file.aiquickdraw.com/mathbot/file/1727054849005tvk87pim.jpg

Let's analyze the graph and the problem provided:

1. **For \( f(9) \):**
   - From the graph, look at the point where \( x = 9 \). The open circle at \( x = 9 \) indicates that the function is undefined at that point. Therefore, \( f(9) = \text{undefined} \).

2. **For \( \lim_{x \to 0} f(x) \):**
   - To find the limit as \( x \) approaches 0, observe the behavior of the function near \( x = 0 \). From the graph, both sides of \( x = 0 \) approach the value \( 3 \), so \( \lim_{x \to 0} f(x) = 3 \).

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Here are the answers based on the graph:

- \( f(9) = \text{undefined} \)
- \( \lim_{x \to 0} f(x) = 3 \)

Let me know if you'd like more details or further clarification!

### Related Questions:
1. How can you identify limits from graphs?
2. What does it mean when a limit "does not exist" (DNE)?
3. What is the significance of open vs. closed circles on a graph?
4. How do you interpret one-sided limits?
5. What role does continuity play in evaluating limits?

**Tip:** Always check whether a function is defined at a specific point by looking for an open or closed circle on the graph!

Evaluate the function f(x) at x = 9 and determine the limits at x = 0, x approaching 9 from the right, and x approaching 4.

Analyze the graph of a function to evaluate f(9), determine limits at x=0 and x=4, and explore one-sided limits approaching x=9 from the right. This problem covers limits, continuity, and the behavior of piecewise functions, suitable for high school students.

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