1. **State the problem:** Find the limit of the function $f(x)$ as $x$ approaches $2$ from the left, i.e., $\lim_{x \to 2^-} f(x)$. 2. **Understand the graph behavior near $x=2$ from the left:** According to the description, the function is constant and equal to $1$ on the interval $(1,2)$ with an open dot at $(2,1)$. This means as $x$ approaches $2$ from values less than $2$, $f(x)$ approaches $1$. 3. **Apply the limit definition:** The left-hand limit at $x=2$ is the value that $f(x)$ approaches as $x$ gets arbitrarily close to $2$ from the left side. Since the function is constant at $1$ just before $2$, the limit is $1$. 4. **Final answer:** $$\lim_{x \to 2^-} f(x) = 1$$