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1. Test 2-type Find the complex zeros of

2. Test 2-type Without solving, determine the character of the solutions of each equation in the complex number system.

a. (2 pts)

b. (2 pts)

c. (2 pts)

3. Solve each of the following absolute value equations:

a. (2 pts)

b. (2 pts)

4. Solve each of the following absolute value inequalities. Give your answer in set-builder and interval notation.

a. (3 pts)

b. (3 pts)

c. (3 pts)

d. (3 pts)

5. Sketch the graph of each of the following. Use transformations of the graph of to graph each function.

a. (4 pts)

b. (4 pts)

6. Let .

a. (2 pts) List each real zero and its multiplicity.

b. (2 pts) Determine whether the graph crosses or touches the x-axis at each x-intercept.

c. (2 pts) Determine the behavior of the graph near each x-intercept.

d. (2 pts) Determine the maximum number of turning points on the graph.

e. (2 pts) Determine the end behavior; that is, find the power function that the graph of f resembles for large values of .

f. (5 pts) Use the information from the above to give a rough sketch of the graph of . 2 bonus points for including the y-intercept.

7. Find the domain and all asymptotes (vertical, horizontal, oblique) for each of the following rational functions.

a. (5 pts)

b. (5 pts)

8. Sketch the graph of each of the following rational functions, using transformations.

a. (5 pts)

b. (5 pts)

9. (15 pts) Sketch the graph of . Show all intercepts, asymptotes and holes.

10. Some followup questions:

a. (5 pts) What is the domain of ?

b. (5 pts) What is the behavior of near x = 4?

c. (5 pts) What is the behavior of near x = 2?