Here is the graph of the function $f(x) = \frac{x}{x^2 - 4}$.

Key Features:

1. Vertical Asymptotes: The function has vertical asymptotes at $x = -2$ and $x = 2$ because the denominator becomes zero at these points.
2. Horizontal Asymptote: The horizontal asymptote is at $y = 0$ because as $x$ approaches infinity, the function approaches zero.
3. Intercepts: The function crosses the origin (0,0), which is the x-intercept as well as the y-intercept.

Would you like more details, or do you have any questions?

Related Questions:

1. What are the steps to find the asymptotes of a rational function?
2. How do you determine the intercepts of a rational function?
3. What happens to the function near the vertical asymptotes?
4. Can the function $f(x)$ ever be undefined? Why?
5. How does the behavior of the function change as $x$ approaches infinity or negative infinity?

Tip:

When sketching the graph of a rational function, always check for vertical and horizontal asymptotes as they are critical for understanding the function's behavior.