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.