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1. (8 pts) Form a polynomial of degree 5, with a zero of multiplicity 1 at x = -3, a zero of multiplicity 2 at x = 4, and a zero of multiplicity 1 at x = 1 + 3i . Please leave it in factored form.

2. (7 pts) Circle the polynomial functions in the list which might have the given graph.

a.

b.

c.

d.

3. (7 pts) Find the domain of .

4. Solve each of the following inequalities. The answers should be strangely similar, yet distinctly different.

a. (5 pts)

b. (5 pts)

5. (7 pts) Use the Remainder Theorem and synthetic division to evaluate for .

6. (7 pts) Use Descartes’ Rule of Signs to determine the possible number of positive and negative real zeros of . You don’t need to find any of the zeros.

7. (7 pts) Use the Rational Zeros Theorem to list all the possible rational zeros of . You don’t need to find which ones (if any) actually work. Just list the possibilities.

8. (7 pts) Use the Intermediate Value Theorem to show that has a zero in the interval .

9. Let .

a. (5 pts) Find
.

b. (5 pts) Find the domain of the composite function .

10. (5 pts) Given that , find functions f and g such that .

11. (10 pts) Find all complex zeros of .

12. (5 pts) Use the complex zeros from #10 to write in factored form.

13. (10 pts) The graph of a one-to-one function f is given. Draw the graph of the inverse function . For convenience (and as a hint), the graph of is given. (This one is fairly tricky).

Bonus Page.

(5 pts) Find a bound on the real zeros of .

(5 pts) Let . Find .