_________________________________ 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.