1. The problem asks us to find the limit of $f(x)$ as $x$ approaches 1, i.e., $\lim_{x \to 1} f(x)$.\n\n2. From the description, the graph of $f(x)$ has an open circle at $(1, 3)$ and a filled point at $(1, 2)$. This implies that $f(1) = 2$ (value of the filled point), but the function approaches a different value near 3 as $x$ approaches 1.\n\n3. The limit depends on the value that $f(x)$ approaches from both sides of $x=1$. The open circle at 3 means the function approaches 3 at $x \to 1$.\n\n4. Since limit looks at the value $f(x)$ approaches as $x$ approaches 1, not necessarily the function value at 1, the limit is $3$.\n\n5. Therefore, $\lim_{x \to 1} f(x) = 3$.\n\nFinal answer: $\boxed{3}$