Here are the graphs for all eight functions as requested:

1. $y = \frac{x^2 + 4}{x}$
2. $y = \frac{x^2 - 4}{2x}$
3. $y = \frac{1}{x + 1} + \frac{1}{x - 1}$
4. $y = \frac{2x}{4 - x^2}$
5. $y = \frac{x^2}{x^2 + 1}$
6. $y = \frac{1}{x^2 + 2x + 3}$
7. $y = \frac{1}{x^2 - 9}$
8. $y = \frac{1}{x^2 - 2x - 8}$

Each graph corresponds to the labeled function and shows different behaviors, such as asymptotes, peaks, and troughs. Would you like further explanations on any specific function or graph behavior?

Here are five related questions:

1. What are the vertical and horizontal asymptotes of these functions?
2. How does the behavior of the graphs change near singularities (undefined points)?
3. What are the domains and ranges for each function?
4. How can you simplify these rational functions algebraically?
5. How does the degree of the numerator and denominator influence the shape of these graphs?

Tip: Always examine the denominator of a rational function to identify where it may be undefined (i.e., potential vertical asymptotes).