1. **State the problem:** We need to find the left-hand limit of the function $f(x)$ as $x$ approaches $-2$, denoted as $\lim_{x \to -2^-} f(x)$. 2. **Understanding limits from graphs:** The left-hand limit means we look at the values of $f(x)$ as $x$ approaches $-2$ from values less than $-2$ (from the left side). 3. **Using the graph:** According to the graph description, the left-hand limit at $x = -2$ is represented by a filled black dot at approximately $y = -3$. 4. **Conclusion:** Since the filled dot at $x = -2$ from the left side is at $y = -3$, the left-hand limit is: $$\lim_{x \to -2^-} f(x) = -3$$ This means as $x$ approaches $-2$ from the left, $f(x)$ approaches $-3$.