1. **Stating the problem:** We are given limits of a function $f(x)$ approaching points $a=2$ and $b=-1$ from the left and right, as well as limits at infinity. We need to find: a) $\lim_{x \to 2^-} f(x)$ b) $\lim_{x \to -1^-} f(x)$ c) $\lim_{x \to -\infty} f(x)$ d) $\lim_{x \to 2^+} f(x)$ e) $\lim_{x \to -1^+} f(x)$ f) $\lim_{x \to +\infty} f(x)$ 2. **Given information from the graph and notation:** - $\lim_{x \to a^-} f(x) = K^-$ means the limit from the left at $x=a$ approaches $K$ from below. - $\lim_{x \to a^+} f(x) = H^-$ means the limit from the right at $x=a$ approaches $H$ from below. - $\lim_{x \to b^-} f(x) = H^-$ and $\lim_{x \to b^+} f(x) = H^+$ indicate limits from left and right at $x=b$. - $\lim_{x \to +\infty} f(x) = K^+$ and $\lim_{x \to -\infty} f(x) = L^-$ indicate horizontal asymptotes. 3. **From the graph and labels:** - At $x=2$ (which is $a$): - Left limit $= K^-$ - Right limit $= H^-$ - At $x=-1$ (which is $b$): - Left limit $= H^-$ - Right limit $= H^+$ - At $x \to +\infty$: limit $= K^+$ - At $x \to -\infty$: limit $= L^-$ 4. **Assigning values from the graph:** - $K$ is on the negative vertical axis, so $K < 0$. - $H$ is on the positive vertical axis, so $H > 0$. - $L$ is below $K$, so $L < K < 0$. 5. **Answering each limit:** a) $\lim_{x \to 2^-} f(x) = K^-$ means the limit approaches $K$ from below, so the value is just below $K$. b) $\lim_{x \to -1^-} f(x) = H^-$ means the limit approaches $H$ from below. c) $\lim_{x \to -\infty} f(x) = L^-$ means the limit approaches $L$ from below. d) $\lim_{x \to 2^+} f(x) = H^-$ means the limit approaches $H$ from below. e) $\lim_{x \to -1^+} f(x) = H^+$ means the limit approaches $H$ from above. f) $\lim_{x \to +\infty} f(x) = K^+$ means the limit approaches $K$ from above. 6. **Summary of limits:** - a) Just below $K$ - b) Just below $H$ - c) Just below $L$ - d) Just below $H$ - e) Just above $H$ - f) Just above $K$ Since exact numeric values are not given, the answers are expressed in terms of $K$, $H$, and $L$ with the indicated approach directions.