1. **State the problem:** Find the asymptotes of the function $$y = x^4 - 8x^2 - 9$$. 2. **Recall the definition of asymptotes:** Asymptotes are lines that the graph of a function approaches as $$x$$ tends to $$\pm \infty$$. 3. **Check for vertical asymptotes:** Vertical asymptotes occur where the function is undefined or tends to infinity. Since $$y = x^4 - 8x^2 - 9$$ is a polynomial, it is defined for all real $$x$$, so there are no vertical asymptotes. 4. **Check for horizontal or oblique asymptotes:** For large $$|x|$$, the highest degree term dominates. Here, the highest degree term is $$x^4$$. 5. **Analyze the behavior as $$x \to \pm \infty$$:** - As $$x \to \infty$$, $$y \approx x^4$$ which tends to $$+\infty$$. - As $$x \to -\infty$$, $$y \approx x^4$$ which also tends to $$+\infty$$. 6. **Conclusion:** Since the function grows without bound and does not approach a finite line, there are no horizontal or oblique asymptotes. **Final answer:** The function $$y = x^4 - 8x^2 - 9$$ has no asymptotes.