1. **State the problem:** We are asked to find the limits of the function $f(x)$ at various points based on the graph description. 2. **Recall the definition of limits:** The limit of $f(x)$ as $x$ approaches a value $a$ is the value that $f(x)$ gets closer to as $x$ gets closer to $a$ from either side (left or right). If the left-hand limit and right-hand limit are equal, the limit exists and equals that value. 3. **Evaluate each limit using the graph description:** - $\lim_{x \to 10^-} f(x) = 0$ (given by the solid dot at $(10,0)$ and the curve approaching this point from the left). - $\lim_{x \to -2^+} f(x) = 3$ (the curve approaches $y=3$ from the right side of $x=-2$). - $\lim_{x \to -8} f(x) = f(-8)$ (the limit equals the function value at $x=-8$ since the curve is continuous there; the local minimum is slightly below $y=-6$ with an open circle, so $f(-8)$ is defined and equals that value). - $\lim_{x \to 6} f(x) = 5$ (the curve approaches $y=5$ near $x=6$; although the local minimum at $x=6$ is marked by an open circle near $y=2$, the limit is the value the function approaches, which is $5$ from the local maximum near $x=7$). 4. **Summary of limits:** $$ \lim_{x \to 10^-} f(x) = 0 \\ \lim_{x \to -2^+} f(x) = 3 \\ \lim_{x \to -8} f(x) = f(-8) \approx -6 \\ \lim_{x \to 6} f(x) = 5 $$ These limits describe the behavior of $f(x)$ near the specified points based on the graph's features.