We mostly looked at functions with polynomials that had asymptotes and holes.
One polynomial had the form of a sum of two cubes, where knowing a related formula is helpful.
To get the coordinates of holes, you plug the x-coordinate that gets a factor of zero in the denominator into the reduced equation.
Finding the behavior close to the asymptote is important, it generally goes up very high or down very low.
To find end behavior, I plug in high magnitude positive and negative numbers. The terms with the highest exponents become more important then.