What are the vertical and horizontal asymptotes for the function f(x) = x² + x - 6/x³ - 1

Solution:

Given function is 

f(x) = [x² + x - 6]/x³ - 1

Vertical asymptote

\(\lim_{x\rightarrow 0}(x^{2}+x-\frac{6}{x^{3}}-1) = -\infty\)

The vertical asymptote in this case is the y axis.i.e. x = 0

There are no horizontal asymptotes for this function.

What are the vertical and horizontal asymptotes for the function f(x) = x² + x - 6/x³ - 1

Summary:

The only asymptote of the function f(x) = x² + x - 6/x³ - 1 is the vertical asymptote in the form of y axis.