Find the horizontal and vertical asymptotes of \( f(x) \). \( I(x)=\frac{x^{8}}{x^{4}+2} \) Find the horizontal asymptotos. Seloct the correct choice and, if necessary, fill in the answer box(es) to complete your choice. A. The function has one horizontal asymptote, (Type an equation.) B. The function has two horizontal asymptotes. The top asymptote is \( \square \) and the bottom asymptote is (Type equations.) C. The function has no horizontal asymptotes.

To find the horizontal asymptotes of the function \( I(x) = \frac{x^{8}}{x^{4}+2} \), we can analyze the degrees of the numerator and denominator. The degree of the numerator (8) is greater than the degree of the denominator (4). In this case, there are no horizontal asymptotes because the function will increase without bound as \( x \) approaches \( \pm \infty \). Therefore, the correct choice is C: The function has no horizontal asymptotes. For the vertical asymptotes, we look for values of \( x \) that make the denominator zero. In this case, \( x^{4} + 2 = 0 \) does not yield any real solutions since \( x^4 \) is always non-negative and cannot equal \(-2\). Thus, there are no vertical asymptotes either.