please please please help with an algebra problem?

Question

Given the following rational function:

f(x)= 2x^3-1 / x^2-16

Find equations for the horizontal or oblique asymptotes if any.

Answer 1

As x becomes infinitely large in either the positive or negative direction, f(x) approaches the line y = 2x because the constant terms are negligible compared to the x^3 and x^2 terms, so the ratio 2x^3 / x^2 = 2x dominates. There is no horizontal asymptote, but there are vertical asymptotes at x = 4 and x = -4 because the denominator has roots there.

Answer 2

Factor the denom: (x-4)(x+4); so there are two vertical asymptotes at x= +-4. An interesting function