1. **State the problem:** We need to find the limit of the function $f(x)$ as $x$ approaches $-1$ from the left, i.e., $\lim_{x \to -1^-} f(x)$. 2. **Understand the graph:** The graph shows a piecewise function with horizontal segments and jump discontinuities. From $x = -2$ to $x = 1$, the function is constant at $y = 0$. 3. **Recall the limit definition:** The left-hand limit $\lim_{x \to a^-} f(x)$ is the value that $f(x)$ approaches as $x$ approaches $a$ from values less than $a$. 4. **Evaluate the limit:** Since for all $x$ just less than $-1$, the function value is $0$ (because the function is constant at $0$ from $-2$ to $1$), the left-hand limit at $x = -1$ is $$\lim_{x \to -1^-} f(x) = 0.$$ 5. **Conclusion:** The limit exists and equals $0$.