Show all work and explain all details

1. Given f(x) = x³ - 4x² - 4x + 16 and g(x)=x⁴ - x³ - 3x² +5x - 2. Answer the following questions for each function and sketch their graphs.
2. List all possible rational zeros of the given function
3. Use Descartes' Rule of Signs to determine the possible number of positive and negative real zeros. State clearly how you computed the number of the changes of the sings and what you use to determine the possible number of negative zeros.
4. Find one rational zero and use long division or synthetic division to find all other real roots. Show all work.
5. Find y-intercepts.
6. Find end behavior. Explain how you do it.
7. Find additional points on each subinterval.
8. Graph the given function. Mark clearly all important points on axis.