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The problem asks for the limit of the function \( f(x) \) as \( x \) approaches \( a = 1 \) using the graph provided.

To determine the limit of \( f(x) \) as \( x \to 1 \), we need to observe the behavior of the function from both sides of \( x = 1 \):
1. **From the left side**: As \( x \to 1^- \) (approaching 1 from the left), the function appears to approach the value \( f(x) = 2 \).
2. **From the right side**: As \( x \to 1^+ \) (approaching 1 from the right), the function also approaches \( f(x) = 2 \).

Since both the left-hand and right-hand limits exist and are equal to 2, the limit of \( f(x) \) as \( x \to 1 \) is:

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

Let me know if you'd like more details, and here are some related questions:

1. How do you calculate one-sided limits from a graph?
2. What if the left-hand and right-hand limits are different?
3. What role do discontinuities play in limits?
4. How would the limit change if there were a vertical asymptote at \( x = 1 \)?
5. What is the precise definition of a limit?

**Tip**: Always check for one-sided limits when analyzing graphs to ensure that both sides converge to the same value.

Use the graph of the given function f to determine the limit at the indicated value of a, if it exists.

Learn how to determine the limit of a function using its graph as x approaches a specific value. This example covers how to analyze the graph of f(x) as x approaches a = 1, ensuring both left-hand and right-hand limits are equal.

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