Given the rational function f(x) = 2x^3 - 7x + 3 / x^2 - 4
a) Determine all of the asymptotes of f(x). Explain your work clearly.
b) Make a neat sketch of f(x). Label all important parts.
I determined that the vertical asymptotes are x = -2, 2 (hopefully I'm right), and there are no horizontal asymptotes. I'm wondering if there is a slant asymptote? How can I tell? If there is one how do I find what the slant asymptote is?
How would the graph look like?
Thanks for your time.