1. **State the problem:** We need to find the limit of the function as $x$ approaches 0 based on the given graph. 2. **Recall the definition of limit:** The limit $\lim_{x \to a} f(x)$ is the value that $f(x)$ approaches as $x$ gets arbitrarily close to $a$ from both sides. 3. **Analyze the graph near $x=0$:** - From the left side ($x \to 0^-$), the graph approaches the solid dot at $(0,1)$. - From the right side ($x \to 0^+$), the graph approaches the open circle at $(0,-1)$. 4. **Check if the left-hand and right-hand limits are equal:** - Left-hand limit: $\lim_{x \to 0^-} f(x) = 1$ - Right-hand limit: $\lim_{x \to 0^+} f(x) = -1$ 5. **Conclusion:** Since the left-hand and right-hand limits are not equal, the two-sided limit does not exist. **Final answer:** DNE