draw the graph of $$ f\left(x\right)\text{ }=\frac{x}{x^2-4} $$

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.

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### 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.

Explore the graph of the function f(x) = x/(x^2 - 4) with detailed insights into its vertical asymptotes at x = -2 and x = 2, horizontal asymptote at y = 0, and intercepts at the origin. Learn about the behavior of rational functions near asymptotes and as x approaches infinity. Suitable for advanced high school students and beyond.

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