1. Problem statement: Evaluate the left-hand limit $\lim_{x\to -2^-} f(x)$ from the given graph. 2. Formula used and important rule: The one-sided left limit is defined by $$\lim_{x\to a^-} f(x)=L$$ which means that as $x$ approaches $a$ from values less than $a$ the values of $f(x)$ approach $L$. 3. Important note: Points plotted exactly at $x=-2$ (closed or open) do not by themselves change the left-hand limit; we only look at the behavior of the curve for $x< -2$ approaching $-2$. 4. Observation from the graph: Tracing the curve and the open points immediately to the left of $x=-2$ shows the y-values approaching $-3$ as $x$ gets closer to $-2$ from the left. 5. Intermediate reasoning: The sequence of y-values for $x< -2$ tends to $-3$ so the left-hand limit equals $-3$. 6. Final answer: $\lim_{x\to -2^-} f(x) = -3$.