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The question asks whether the statement \(\lim_{x \to 0} f(x)\) exists is true or false, and we have a graph of the function to analyze this limit.

### Analysis of the Graph:
To determine if the limit \(\lim_{x \to 0} f(x)\) exists, we need to check the left-hand limit (\(\lim_{x \to 0^-} f(x)\)) and the right-hand limit (\(\lim_{x \to 0^+} f(x)\)).

- **Left-hand limit** (\(\lim_{x \to 0^-} f(x)\)):
  From the left of \(x = 0\), the graph shows that as \(x\) approaches 0, the function approaches \(f(x) = -2\).
  
- **Right-hand limit** (\(\lim_{x \to 0^+} f(x)\)):
  From the right of \(x = 0\), the graph shows that as \(x\) approaches 0, the function also approaches \(f(x) = -2\).

Since both the left-hand and right-hand limits are equal to \(-2\), the overall limit \(\lim_{x \to 0} f(x)\) exists and is equal to \(-2\).

### Answer:
The statement \(\lim_{x \to 0} f(x)\) exists is **true**.

Would you like further details or explanations on this? Here are some related questions:

1. What does it mean for a limit to exist at a certain point?
2. How do you determine limits graphically?
3. What are left-hand and right-hand limits?
4. How would the answer change if the limits from both sides were not equal?
5. How does the continuity of a function relate to the existence of a limit?

**Tip:** When finding limits graphically, always compare the values from both the left and right sides of the point of interest.

The statement 'lim f(x) exists as x approaches 0' is true or false based on the provided graph.

Learn how to determine if a limit exists using graphical analysis. This problem focuses on the existence of limits by comparing left-hand and right-hand values of the function as x approaches 0. Suitable for high school students in Grades 10-12.

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