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To determine \(\lim_{x \to 0} f(x)\) from the given graph, we need to analyze the behavior of the function \(f(x)\) as \(x\) approaches 0 from both the left (\(x \to 0^-\)) and the right (\(x \to 0^+\)).

- **As \(x \to 0^-\) (approaching 0 from the left)**: The graph shows that as \(x\) gets closer to 0 from the negative side, the function \(f(x)\) approaches 2.
  
- **As \(x \to 0^+\) (approaching 0 from the right)**: The graph indicates that as \(x\) gets closer to 0 from the positive side, the function \(f(x)\) also approaches 2.

Since both the left-hand limit and the right-hand limit as \(x\) approaches 0 are equal and both equal to 2, we conclude:

\[
\lim_{x \to 0} f(x) = 2
\]

Would you like more details or have any other questions?

Here are some related questions:
1. What is the definition of a limit in calculus?
2. How do you find the limit of a function graphically?
3. What is the significance of one-sided limits?
4. How do discontinuities affect the existence of limits?
5. Can a function have a limit at a point where it is not defined?

**Tip:** When determining limits graphically, always check the behavior of the function from both sides of the point in question to ensure consistency in the limit value.

In this calculus problem, learn how to find the limit of a function graphically as x approaches 0. Analyze the behavior of the function from both sides and conclude that the limit equals 2. This problem covers key concepts in limits and continuity, suitable for high school calculus students.

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