1. The problem asks to find the limits of the function $f(x)$ at specific points and identify vertical asymptotes. 2. Limits describe the behavior of $f(x)$ as $x$ approaches a certain value. 3. Vertical asymptotes occur where $f(x)$ approaches $\pm \infty$ as $x$ approaches a certain value. 4. From the graph description: (a) $\lim_{x \to -7} f(x) = -\infty$ (given) (b) $\lim_{x \to -3} f(x) = \infty$ (given) (c) $\lim_{x \to 0} f(x)$: The graph crosses the y-axis and oscillates between positive and negative values near $x=0$, so the limit exists and is finite. From the graph, $f(0) \approx 2$. (d) $\lim_{x \to 6^-} f(x)$: Approaching 6 from the left, the function tends to $-\infty$ (from the description of vertical asymptote behavior). (e) $\lim_{x \to 6^+} f(x)$: Approaching 6 from the right, the function tends to $\infty$. (f) Vertical asymptotes occur where limits tend to infinity or negative infinity. From the graph, these are at $x = -7, -3, 6$. Final answers: (a) $-\infty$ (b) $\infty$ (c) $2$ (d) $-\infty$ (e) $\infty$ (f) $x = -7, -3, 6$