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From the image provided, you are asked to determine the value of the limit of a function \( f(x) \) as \( x \) approaches 2. The mathematical expression is:

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

By analyzing the graph of the function \( f(x) \), let’s check the behavior of the function as \( x \) approaches 2 from both the left-hand side and the right-hand side:

- **Left-hand limit**: As \( x \) approaches 2 from the left (\( x \to 2^- \)), the function seems to approach a value of \( 1 \).
- **Right-hand limit**: As \( x \) approaches 2 from the right (\( x \to 2^+ \)), the function also seems to approach \( 1 \).

Since both the left-hand and right-hand limits approach the same value, we conclude that:

\[
\lim_{x \to 2} f(x) = 1
\]

Thus, the value of the limit is \( 1 \).

Let me know if you need further details or have any questions.

### 5 related questions:
1. How do you calculate a limit using a graph when the function behaves differently from the left and right?
2. What does it mean if the left-hand and right-hand limits do not match?
3. Can a limit exist if there is a hole or discontinuity at a specific point in the graph?
4. What is the difference between the limit of a function and the value of a function at a point?
5. How does the concept of limits help in understanding derivatives?

### Tip: 
When dealing with limits graphically, always inspect both the left-hand and right-hand behavior to determine if they converge to the same value.

Determine the value of lim x→2 f(x) based on the provided graph.

Analyze the graph of the function f(x) to calculate the limit as x approaches 2. Learn how to determine left-hand and right-hand limits from graphs in this calculus-based problem, suitable for Grades 10-12.

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