Analyzing the Graph:

1. Horizontal Asymptote:

   • A horizontal asymptote occurs when the function levels off as $x \to \pm \infty$.
   • From the graph, it is clear that the function approaches the line $y = 0$ (the x-axis) as $x \to \pm \infty$.

   Horizontal Asymptote: $y = 0$.

2. Vertical Asymptote:

   • A vertical asymptote occurs when the function approaches infinity as $x$ approaches a specific value.
   • From the graph, the vertical asymptote is located at $x = 2$ because the graph diverges as it nears $x = 2$.

   Vertical Asymptote: $x = 2$.

3. Domain of the Function:

   • The domain includes all $x$-values except where the vertical asymptote occurs.
   • Since there is a vertical asymptote at $x = 2$, the domain excludes $x = 2$.

   Domain: $x \in (-\infty, 2) \cup (2, \infty)$.

Final Answers:

1. Horizontal Asymptote: $y = 0$.
2. Vertical Asymptote: $x = 2$.
3. Domain: $x \in (-\infty, 2) \cup (2, \infty)$.

Would you like further explanations about asymptotes or domains? Let me know!

Related Questions:

1. How do you find horizontal asymptotes from a rational function analytically?
2. What is the behavior of a rational function near its vertical asymptote?
3. How can you determine the domain of a rational function algebraically?
4. Can a function have more than one vertical asymptote?
5. What happens if the degrees of the numerator and denominator in a rational function are equal?

Tip: The vertical asymptote occurs where the denominator of the rational function equals zero. Always check for these critical points.