1. **State the problem:** Determine if the function $f(x) = x^4 - x^2$ has a horizontal asymptote. 2. **Recall the definition of horizontal asymptotes:** A horizontal asymptote is a horizontal line $y = L$ where $\lim_{x \to \infty} f(x) = L$ or $\lim_{x \to -\infty} f(x) = L$. 3. **Calculate the limits at infinity:** $$\lim_{x \to \infty} (x^4 - x^2)$$ Since $x^4$ grows faster than $x^2$, the dominant term is $x^4$ which tends to $+\infty$ as $x \to \infty$. Therefore, $$\lim_{x \to \infty} (x^4 - x^2) = +\infty$$ 4. **Calculate the limit at negative infinity:** $$\lim_{x \to -\infty} (x^4 - x^2)$$ Note that $x^4$ is always positive and grows large as $x \to -\infty$, and $x^2$ is also positive. Thus, $$\lim_{x \to -\infty} (x^4 - x^2) = +\infty$$ 5. **Conclusion:** Since both limits tend to infinity, the function does not approach a finite constant value at infinity or negative infinity. Therefore, **the function $f(x) = x^4 - x^2$ has no horizontal asymptote.** 6. **Addressing the question about 1:** The limit is not 1; it diverges to infinity, so the horizontal asymptote is not $y=1$.