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Answer: Choice C) 2x^4</h3>
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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.
