https://file.aiquickdraw.com/mathbot/file/17268949160861yxh5sph.jpg

Here is the graph of the piecewise function based on the given description:

- The blue line represents \( f(x) = x - 1 \) for \( x \leq 2 \), with a solid dot at \( (2, 1) \).
- The green line represents \( f(x) = 2x - 3 \) for \( x > 2 \), with an open dot at \( (2, 1) \).

This visual confirms that the function has a continuous limit at \( x = 2 \), as both the left and right-hand limits converge to \( f(2) = 1 \).

Would you like more details or have any questions?

Here are 5 follow-up questions:
1. What is the definition of continuity for a function at a point?
2. How can we calculate the left-hand and right-hand limits of a function?
3. Why is the dot at \( (2, 1) \) open on the right side of the piecewise function?
4. What conditions ensure a function is continuous at a given point?
5. Can a function be differentiable if it has an open dot at some point?

**Tip:** In piecewise functions, always check for both limits and function value at the boundary to assess continuity.

This solution provides a graph of a piecewise function f(x) = x - 1 for x ≤ 2 and f(x) = 2x - 3 for x > 2. It explains the concept of continuity at x = 2 and evaluates the left and right-hand limits, concluding that the function has a continuous limit at x = 2.

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