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.