Answer
X-intercept requires that there are real zeros when y=0, while the function has a numerator of
$x^6+10\gt0$ for all $x\in R$
A horizontal asymptote requires a limiting value when $x\to \pm\infty$, while this function has
end behaviors of $x\to\pm\infty,y\to\infty$ for all $x\in R$
A vertical asymptote requires that the denominator has at least one zero, while the denominator of this function is $x^4+8x^2+15=(x^2+3)(x^+5)\gt0$
A slant asymptote requires that the order of the numerator is 1 higher than the denominator, a condition
not satisfied by this function.
Since the numerator is 2 orders higher than the denominator, the end behaviors of this function will be
similar to those of a parabola.
Work Step by Step
see above.
