1. **State the problem:** We are asked to find the limits of the function $g(x)$ as $x$ approaches positive and negative infinity, and to identify the horizontal asymptote(s) of $g(x)$ based on the graph description. 2. **Analyze the limit as $x \to \infty$:** The graph shows that as $x$ goes to positive infinity, $g(x)$ approaches $y=0$. This means: $$\lim_{x \to \infty} g(x) = 0$$ 3. **Analyze the limit as $x \to -\infty$:** The graph starts near negative infinity with a sharp increase, indicating that as $x$ goes to negative infinity, $g(x)$ tends to negative infinity: $$\lim_{x \to -\infty} g(x) = -\infty$$ 4. **Identify horizontal asymptote(s):** A horizontal asymptote is a horizontal line that the graph approaches as $x$ goes to $\pm \infty$. Since $g(x)$ approaches $y=0$ as $x \to \infty$, the horizontal asymptote is: $$y = 0$$ 5. **Summary:** - $\lim_{x \to \infty} g(x) = 0$ - $\lim_{x \to -\infty} g(x) = -\infty$ - Horizontal asymptote: $y=0$ This matches the graph description where the curve approaches zero on the right and decreases without bound on the left.