1. The problem asks for the limit of the function $f(x)$ as $x$ approaches 6. 2. The limit of $f(x)$ as $x$ approaches a value $a$ is the value that $f(x)$ gets closer to as $x$ gets closer to $a$ from both sides. 3. To find $\lim_{x \to 6} f(x)$, we look at the behavior of $f(x)$ near $x=6$. 4. From the graph (as described), if the left-hand limit and right-hand limit at $x=6$ are equal, that value is the limit. 5. If the graph shows $f(x)$ approaching 3 from both sides as $x$ approaches 6, then $\lim_{x \to 6} f(x) = 3$. 6. Therefore, the limit is 3, which corresponds to answer choice D.