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MATH 2412 EXAM 1 06/15/2010
DO ALL WORK ON THIS EXAM. BE SURE YOUR PHONE IS OFF. OBSERVE PROPER EXAM DEMEANOR.
DETERMINE THE END BEHAVIOR OF EACH OF THE FOLLOWING.
1. f  x   2x99  4x90
2. f  x   3x6  5x3  1
3. Find the x and y intercepts of f  x   2x3  3x2  x .
4. Test f  x   x3  x for symmetry with respect to the y-axis and origin.
5. Graph f  x   x 4  1 using the method presented in the text.


6. Use long division to divide 12x 3  10x 2  8x  4 by 2 x  1 .


7. Use synthetic division to divide 6 x 3  5x  3 by  x  1 .
8. For P  x   3x 4  14x3  14x2  8x  8,
a. state the set of possible rational zeros.
b. Using synthetic division, find two zeros.
c. Find the remaining zeros by factoring or the quadratic formula.
Graph each rational function. State the equations of the vertical and horizontal asymptotes and
indicate each on your graph.
9. f  x  
2x
x 2  3x  4
10. f  x  
10x  1
2x  3
11. For f  x  
2x 2  x  2
,
x 1
a. state the equations of the vertical and oblique asymptotes.
b. draw the graph.
12. Expand log6
a2 c
by using the properties of logarithms.
b5
13. Write 2log3  4log2 
1
log16 as a single log in simplest form.
2
SOLVE BY USING LOGARITHMS. ROUND YOUR SOLUTION TO FOUR DECIMAL PLACES.
14. 2.83 x 5  13
15. e0.3 x 5  1.2
SOLVE.
16. log11  log3  log 2 x  3
17. log2 x  log2  x  2   3
18. An experiment begins with 1000 bacteria. After 2 hrs, there are 700.
a. Find the decay rate. Round to 4 decimal places.
b. Determine the number after 5 hrs.