with undefined points at the roots of

There will be 1, 2, or 3 real solutions to this equation. Explicit solutions for the roots of a cubic polynomial are complicated and not given here. Many mathematical and statistical software programs can determine the roots of a polynomial equation numerically, and it is recommended that you use one these programs if you need to know where these roots occur.

with the exception that y = may be excluded.

and vertical asymptotes at the roots of

There will be 1, 2, or 3 real solutions to this equation. Explicit solutions for the roots of a cubic polynomial are complicated and not given here. Many mathematical and statistical software programs can determine the roots of a polynomial equation numerically, and it is recommended that you use one these programs if you need to know where these roots occur.