https://file.aiquickdraw.com/mathbot/file/1726892903594ux2fvug7.jpg

https://file.aiquickdraw.com/mathbot/file/1726892923477u0hu36x1.jpg

From the graph shown, we are asked to determine:

\[
\lim_{x \to 2} f(x)
\]

### Analyzing the Graph:
- As \( x \to 2 \) from the left (\( x \to 2^{-} \)):
  - The graph approaches \( y = 3 \).
- As \( x \to 2 \) from the right (\( x \to 2^{+} \)):
  - The graph approaches \( y = 1 \).

### Conclusion:
Since the left-hand limit and the right-hand limit as \( x \to 2 \) are different, the overall limit **does not exist**.

\[
\lim_{x \to 2} f(x) \quad \text{does not exist}.
\]

Would you like a more detailed explanation on limits? Here are some additional questions that could expand your understanding:

1. What are the conditions for the existence of a limit?
2. How can we calculate one-sided limits?
3. What is the difference between limits and continuity at a point?
4. How do discontinuities like jumps or holes affect limits?
5. Can a limit exist if the function is undefined at the point?

**Tip:** When both the left-hand and right-hand limits differ, the two-sided limit does not exist.

Determine the limit of the function f(x) as x approaches 2 from the graph provided.

Explore the concept of limits with a graphical analysis of a function as x approaches 2, showing how different one-sided limits indicate the non-existence of the limit at the point. This example provides a clear illustration of discontinuity and piecewise functions in calculus.

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