1. **Problem:** Given the function $$f(x) = xe^x$$, find the domain and asymptotes. 2. **Domain:** The function $$f(x) = xe^x$$ is defined for all real numbers because both $$x$$ and $$e^x$$ are defined everywhere. \[ \text{Domain} = (-\infty, \infty) \] 3. **Asymptotes:** - As $$x \to \infty$$, $$xe^x \to \infty$$, so no horizontal asymptote. - As $$x \to -\infty$$, $$e^x \to 0$$ and $$x \to -\infty$$, so $$xe^x \to 0$$ because exponential decay dominates linear growth. Thus, the horizontal asymptote is: $$y = 0$$ as $$x \to -\infty$$. No vertical asymptotes exist because the function is defined everywhere. 4. **Summary:** - Domain: $$(-\infty, \infty)$$ - Horizontal asymptote: $$y=0$$ as $$x \to -\infty$$ - No vertical asymptotes. Final answer: $$\boxed{\text{Domain} = (-\infty, \infty), \quad \text{Horizontal asymptote: } y=0 \text{ as } x \to -\infty}$$