https://file.aiquickdraw.com/mathbot/file/1727305710892uz2ot8fe.jpg

Here is the graph based on the table you provided. The different regions are highlighted:

- **Yellow Region (x < 0):** As \( x \) approaches 0 from the left, \( f(x) \) approaches 0.
- **Blue Region (0 ≤ x < 2):** As \( x \) moves closer to 1, \( f(x) \) approaches 1.
- **Orange Region (x > 2):** As \( x \) increases beyond 2, \( f(x) \) approaches 2.

Let me know if you'd like any further explanation or details.

Here are 5 related questions to explore further:
1. What is the behavior of the function as \( x \) approaches 1?
2. How does the function behave as \( x \) approaches 2 from the left and right?
3. Can we define a piecewise function for the given data?
4. What is the derivative of the function at \( x = 1 \)?
5. How would the graph change if \( x \) had values between 0 and -1 more densely?

**Tip:** In such graphs, always look at the behavior around critical points like \( x = 0 \), \( x = 1 \), and \( x = 2 \), as these determine the limit behavior.

Explore the graph of a piecewise function based on limit behavior at critical points. Understand how f(x) approaches 0, 1, and 2 for different ranges of x, with detailed explanations and data points.

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