The function given is:

$f(x) = \frac{4x - 3}{x^2 + 4}$

Would you like me to evaluate this function, find its critical points, analyze its behavior, or perform some other specific operation? Let me know what you're looking to explore!

Here are some possible directions you might want to consider:

1. Find the domain of the function.
2. Determine the function's critical points and analyze its local extrema.
3. Find the asymptotes (horizontal, vertical, or oblique) of the function.
4. Evaluate the function for specific values of $x$.
5. Determine the intervals of increase and decrease.

Tip: To understand a function thoroughly, analyzing its critical points and asymptotes often provides valuable insights into its overall behavior.