Mat 121-003 C3 Test Due Mon 11/13/06 @ 1pm NAME ____________________________
For full credit, you MUST show all work. Use a separate piece of paper and clearly label each problem.
Late submissions will lose 1% per hour after 1pm.
Consider the polynomial, f(x) = x5 +3x4 +x3 –x2 -4
1. List all of the possible rational roots of this polynomial.
2. Find all the rational roots using synthetic division; list the multiplicity of each root.
3. Using synthetic division, show that the complex roots i are roots of this polynomial.
4. Solve f(x) 0
5. Plot f(x)
6. Write f(x) in factored form, then explain, using numerical examples, why f(x) changes sign for some of
the zeroes and not for others.
Consider the rational function g(x) =
3 ( )x2x
( )x4
2
7. Plot g(x). Specify the zeroes, asymptotes, and large x behavior.
8. Solve g(x) 0.
9. Explain why, using numerical examples, why g(x) goes to near the asymptote(s).
The concentration, C, of a certain drug in a patient’s bloodstream obeys C(t) =
0.5 t200
8t200
, where t is the
time in hours after administering the drug.
10. Plot C(t) for positive t values.
11. For what positive t values is C(t) > 0.5? When a pharmaceutical company publishes this value, what
would they say it means?
12. Find the large t behavior. What would the physician or pharmacist tell the patient this means?
13. Find the domain of h(x) =
x33x2
, i.e., for what x values is this function defined?
14. Plot h(x).
I, __________________________________________________, assert that I used no live help on this test.
