From the graph you provided, it appears to be a rational function with vertical and horizontal asymptotes.

Vertical Asymptotes:

The graph shows two vertical lines approaching $x = -1$ and $x = 3$, which indicates vertical asymptotes at these points.

Horizontal Asymptote:

The graph approaches $y = 0$ as $x \to \infty$ and $x \to -\infty$, indicating a horizontal asymptote at $y = 0$.

Conclusion:

Based on the graph, the correct asymptotes are:

• $x = -1$
• $x = 3$
• $y = 0$

Answer Choices:

• $x = -1$ ✔️
• $y = -2$ ✖️ (not an asymptote)
• $x = 3$ ✔️
• $x = 0$ ✖️ (not an asymptote)
• $y = 0$ ✔️
• $y = -3$ ✖️ (not an asymptote)

Would you like further explanation on asymptotes, or do you have any questions?

Here are 5 related questions to deepen your understanding:

1. How do vertical asymptotes differ from horizontal asymptotes?
2. What is the equation of a rational function with the same asymptotes as shown in the graph?
3. How can you identify asymptotes algebraically from a rational function?
4. Why do rational functions often have vertical asymptotes?
5. How would the graph change if there was a slant asymptote instead of a horizontal asymptote?

Tip: Asymptotes describe the behavior of a function as it approaches infinity or specific points where the function is undefined.