1. **State the problem:** We are asked to determine which limit expressions agree with the graph of the function $f$ that has vertical asymptotes near $x = -5, 1, 3,$ and $5$. Specifically, we want to check the behavior of $f(x)$ as $x$ approaches $1$ from the left, $3$ from the right, and $5$ from the left. 2. **Recall the definition of limits at vertical asymptotes:** When a function approaches a vertical asymptote at $x = a$, the limit of $f(x)$ as $x$ approaches $a$ from one side can be $+$ or $-$ depending on the direction the function goes. 3. **Analyze each limit:** - For $\lim_{x \to 1^-} f(x)$, the graph shows $f(x) \to -\infty$ as $x$ approaches $1$ from the left. - For $\lim_{x \to 3^+} f(x)$, the graph shows $f(x) \to -\infty$ as $x$ approaches $3$ from the right. - For $\lim_{x \to 5^-} f(x)$, the graph shows $f(x) \to -\infty$ as $x$ approaches $5$ from the left. 4. **Conclusion:** All three limit expressions A, B, and C correctly describe the behavior of $f(x)$ near the vertical asymptotes. **Final answer:** A, B, and C are all correct.