The equation of the horizontal asymptote for the function \( G(x) = \frac{2x^2}{x^3 - 5} \) is:

\[
y = 0
\]

This is because the degree of the numerator (2) is less than the degree of the denominator (3).

If you have any further questions or need additional details, feel free to ask!

Here are 5 related questions that expand on this topic:

1. How can you verify the horizontal asymptote by evaluating the limits as \( x \) approaches infinity?
2. What are the conditions for a rational function to have a horizontal asymptote at \( y = 1 \)?
3. How would the horizontal asymptote change if the degree of the numerator and denominator were the same?
4. What role do horizontal asymptotes play in graphing rational functions?
5. How do horizontal asymptotes relate to end behavior in polynomial functions?

**Tip:** For rational functions, understanding how the function behaves as \( x \) approaches positive or negative infinity helps in determining the horizontal asymptote.

Explore the concept of horizontal asymptotes in rational functions using the example of G(x) = 2x^2 / (x^3 - 5). Learn how to determine the equation of the horizontal asymptote and its implications. Suitable for advanced high school students and college-level learners.

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