1. **Stating the problem:** We need to find the limits of the function $f(x)$ at various points based on the graph. 2. **Recall limit definitions:** - The limit $\lim_{x \to a} f(x)$ is the value that $f(x)$ approaches as $x$ gets arbitrarily close to $a$. - The left-hand limit $\lim_{x \to a^-} f(x)$ is the value $f(x)$ approaches as $x$ approaches $a$ from the left. - The right-hand limit $\lim_{x \to a^+} f(x)$ is the value $f(x)$ approaches as $x$ approaches $a$ from the right. - If left and right limits differ, the two-sided limit does not exist. 3. **Analyze each limit from the graph:** **a.** $\lim_{x \to 0} f(x)$: The graph approaches $y=3$ near $x=0$ with a dashed line, indicating the limit is 3. **b.** $\lim_{x \to 1^-} f(x)$: Approaching $x=1$ from the left, the graph rises steeply to about $y=6$. **c.** $\lim_{x \to 1^+} f(x)$: Approaching $x=1$ from the right, the graph slopes downward from the open circle at $y=4$ and continues smoothly, so the right limit is $4$. **d.** $\lim_{x \to 1} f(x)$: Since left limit ($6$) and right limit ($4$) differ, the two-sided limit does not exist. **e.** $\lim_{x \to +\infty} f(x)$: The graph declines toward zero as $x$ goes to infinity, so the limit is $0$. 4. **Final answers:** $$ \begin{aligned} &\text{a. } \lim_{x \to 0} f(x) = 3 \\ &\text{b. } \lim_{x \to 1^-} f(x) = 6 \\ &\text{c. } \lim_{x \to 1^+} f(x) = 4 \\ &\text{d. } \lim_{x \to 1} f(x) \text{ does not exist} \\ &\text{e. } \lim_{x \to +\infty} f(x) = 0 \end{aligned} $$