1. **State the problem:** We are given the function $f(x) = -\frac{1}{x+1}$ and asked to verify if the described graph properties are correct. 2. **Recall the function properties:** - The function is a rational function with a denominator $x+1$. - Vertical asymptotes occur where the denominator is zero, so at $x = -1$. - Horizontal asymptotes for rational functions where the degree of numerator is less than denominator is $y=0$. 3. **Check vertical asymptote:** - Since $x+1=0$ at $x=-1$, the function is undefined there, confirming a vertical asymptote at $x=-1$. 4. **Check horizontal asymptote:** - As $x \to \pm \infty$, $f(x) = -\frac{1}{x+1} \to 0$, so horizontal asymptote is $y=0$. 5. **Analyze branches:** - For $x < -1$, $x+1$ is negative, so $f(x) = -\frac{1}{\text{negative}} = \text{positive}$, so the graph is above the $x$-axis on the left side. - For $x > -1$, $x+1$ is positive, so $f(x) = -\frac{1}{\text{positive}} = \text{negative}$, so the graph is below the $x$-axis on the right side. 6. **Conclusion:** The description matches the function's behavior: vertical asymptote at $x=-1$, horizontal asymptote at $y=0$, upper branch on the left side curving upwards, and lower branch on the right side curving downwards. **Final answer:** Yes, the description of the graph is correct.