To find the horizontal asymptote of the function $G(x) = \frac{2x^2}{x^3 - 5}$, we analyze the degrees of the numerator and denominator.

Step-by-Step Process:

1. Identify the degrees of the numerator and denominator:

   • The numerator $2x^2$ is of degree 2.
   • The denominator $x^3 - 5$ is of degree 3.

2. Compare the degrees:

   • The degree of the numerator (2) is less than the degree of the denominator (3).

3. Conclusion about the horizontal asymptote:

   • When the degree of the numerator is less than the degree of the denominator, the horizontal asymptote is $y = 0$.

So, the horizontal asymptote of $G(x)$ is $y = 0$.

Would you like further details or explanations on any part of this process?

Here are 5 related questions that expand on this topic:

1. What are the vertical asymptotes of the function $G(x)$?
2. How do you find the horizontal asymptote if the degrees of the numerator and denominator are equal?
3. What is the behavior of the function $G(x)$ as $x$ approaches infinity?
4. Can you explain how to find oblique asymptotes in rational functions?
5. How do horizontal asymptotes differ from vertical asymptotes in terms of function behavior?

Tip: When analyzing rational functions for asymptotes, always compare the degrees of the numerator and denominator first. This gives you quick insights into the horizontal or slant asymptotes.