An end behavior model for f(x) =

As x gets larger and larger, all we really care about is the leading terms. This is because 8x^6 is much larger than -16x^3 and 8 for very very large x values. The larger the exponent, the larger the result will be.

So effectively, the leading term 8x^6 dictates the end behavior for the numerator.

In a similar way, the leading term 4x^2 dictates the end behavior for the denominator polynomial.

Divide the two leading terms:

(8x^6)/(4x^2) = (8/4)*x^(6-2) = 2x^4

The rule used here is (a^b)/(a^c) = a^(b-c)

So as x goes to infinity or negative infinity, it's slowly approaching the asymptote y = 2x^4.

the correct answer is the second option