Let's analyze the graph and answer the questions.

1. Domain of the function: The function has a vertical asymptote at $x = 1$ (as indicated by the dashed red line). The function is undefined at $x = 1$ but is defined for all other values of $x$. Therefore, the domain of the function is: $(-\infty, 1) \cup (1, \infty)$

2. Equation of the vertical asymptote: The vertical asymptote occurs where the function approaches infinity or negative infinity, which happens at $x = 1$. Therefore, the equation of the vertical asymptote is: $x = 1$

3. Equation of the horizontal asymptote: As $x$ approaches very large positive or negative values, the function seems to approach $y = 0$. Thus, the equation of the horizontal asymptote is: $y = 0$

Let me know if you would like further details!

Here are five related questions to extend your understanding:

1. What type of function usually has a vertical asymptote?
2. How can you find vertical asymptotes algebraically for rational functions?
3. What happens to the function's values as $x$ approaches the vertical asymptote from the left or right?
4. Can a function have more than one vertical or horizontal asymptote?
5. How do vertical and horizontal asymptotes help in sketching the graph of a function?

Tip: Vertical asymptotes typically occur where the denominator of a rational function equals zero, provided it doesn't cancel with the numerator.