So far, you have used synthetic division and factoring to find x-intercepts. What additional information do you need to create an accurate sketch of the function ? How do you propose we find this information using the equation ?

Answer 1

The y-intercepts are of great help.
It also helps to have an idea what the general shape of different polynomials are.
e.g. A fourth degree generally has the shape of a W , etc
Also a reasonable number of ordered pairs can be calculate and plotted to show the shape of the function.
I would also consider vertical and horizontal asymptotes.