1. **State the problem:** We need to find the horizontal asymptote of the rational function $$y = \frac{2}{x + 1}$$ and sketch its graph. 2. **Recall the rule for horizontal asymptotes:** For a rational function $$\frac{P(x)}{Q(x)}$$ where the degree of $$P(x)$$ is less than the degree of $$Q(x)$$, the horizontal asymptote is $$y = 0$$. 3. **Apply the rule:** Here, the numerator is a constant (degree 0) and the denominator is degree 1, so the horizontal asymptote is $$y = 0$$. 4. **Vertical asymptote:** The denominator equals zero at $$x = -1$$, so there is a vertical asymptote at $$x = -1$$. 5. **Summary:** - Vertical asymptote: $$x = -1$$ - Horizontal asymptote: $$y = 0$$ 6. **Graph behavior:** As $$x \to \infty$$ or $$x \to -\infty$$, $$y \to 0$$. **Final answer:** The horizontal asymptote is $$y = 0$$.