1. **State the problem:** We are given limits related to the function $h(x)$ and asked to determine specific limit values and function behavior based on a described graph. 2. **Given limits near $x=5$: ** - The right-hand limit as $x$ approaches 5 from the right, $\lim_{x \to 5^+} h(x) = 3$. - The two-sided limit at $x=5$, $\lim_{x \to 5} h(x) = 4$. 3. **Interpretation:** - Since the right-hand limit is 3 but the overall limit at 5 is 4, the left-hand limit at 5 must be 4 (to have the two-sided limit equal to 4). - This indicates a jump discontinuity at $x=5$. 4. **Next, analyze the limit at $x = -3$ from the left:** - The graph shows a point near $(-3,4)$ marked. - To find $\lim_{x \to -3^-} h(x)$, look at the values of $h(x)$ approaching $-3$ from the left. - The graph description says that the function rises from $y \approx 0$ at $x=-4$ to a peak at $(-3,4)$. - Therefore, from the left of $-3$, $h(x)$ approaches 4. 5. **Final answers:** - $\lim_{x \to 5^+} h(x) = 3$ - $\lim_{x \to 5} h(x) = 4$ - $\lim_{x \to -3^-} h(x) = 4$ These values exist and are based on the behavior of the function described.