To determine the asymptotes of the function depicted in the graph, let's analyze the behavior of the function:

1. Vertical Asymptotes: These occur where the function approaches infinity or negative infinity as $x$ approaches a particular value.

   • The graph shows vertical asymptotes at $x = -3$ and $x = 3$, as the function approaches $\infty$ as $x$ approaches these values from the left and right.

2. Horizontal Asymptotes: These occur when the function approaches a particular $y$-value as $x$ approaches infinity or negative infinity.

   • The graph approaches $y = 0$ as $x$ moves towards positive or negative infinity. Therefore, there is a horizontal asymptote at $y = 0$.

Given these observations, the correct selections for the asymptotes are:

• $x = 3$ (vertical asymptote)
• $y = 0$ (horizontal asymptote)

The correct choices from your list are:

• c. $x = 3$
• e. $y = 0$

Would you like further details or have any questions?

Here are 5 related questions to expand your understanding:

1. What are the equations of the asymptotes for a hyperbola centered at the origin?
2. How do you determine the vertical asymptotes of a rational function?
3. What is the significance of horizontal asymptotes in the behavior of functions as $x$ approaches infinity?
4. Can a function have more than one horizontal asymptote?
5. How do you find oblique (slant) asymptotes for a rational function?

Tip: When identifying asymptotes, always look for where the function behaves abnormally, such as rising or falling steeply, or flattening out at the extremes of the graph.