1. AIM: HOW DO WE INVESTIGATE THE BEHAVIOR OF POLYNOMIAL INEQUALITIES? ***An alternate approach to solving polynomial inequalities.*** HW p. A73 #55, 61 1 FLASHBACK Do Now: Solve for x

2. AIM: HOW DO WE INVESTIGATE THE BEHAVIOR OF POLYNOMIAL INEQUALITIES? ***An alternate approach to solving polynomial inequalities.*** HW p. A73 #55, 61 2 Do Now: Display solution on a number line and in interval notation

3. AIM: HOW DO WE INVESTIGATE THE BEHAVIOR OF POLYNOMIAL INEQUALITIES? ***An alternate approach to solving polynomial inequalities.*** HW p. A73 #55, 61 3 CRITICAL VALUES TEST INTERVALS (possible solutions) Pick a number from each interval and test in the inequality. We are looking for the intervals where the function is > 0 -5 02 0 2 TEST INTERVALS PICK x- value POLYNONIAL VALUE CONLC. SOLVE by finding the critical values and testing the intervals

4. AIM: HOW DO WE INVESTIGATE THE BEHAVIOR OF POLYNOMIAL INEQUALITIES? ***An alternate approach to solving polynomial inequalities.*** HW p. A73 #55, 61 4 SOLVE by finding the critical values and testing the intervals

5. AIM: HOW DO WE INVESTIGATE THE BEHAVIOR OF POLYNOMIAL INEQUALITIES? ***An alternate approach to solving polynomial inequalities.*** HW p. A73 #55, 61 5 What if the original example was: HW #55 OR, Alternately:

6. AIM: HOW DO WE INVESTIGATE THE BEHAVIOR OF POLYNOMIAL INEQUALITIES? ***An alternate approach to solving polynomial inequalities.*** HW p. A73 #55, 61 6 HW #61

7. AIM: HOW DO WE INVESTIGATE THE BEHAVIOR OF POLYNOMIAL INEQUALITIES? ***An alternate approach to solving polynomial inequalities.*** HW p. A73 #55, 61 7 Some more examples of Polynomial Inequalities on p. A73 NO SOLUTION; there are no x-values such that the polynomial evaluates to a number below 0. #59) #60) SOLUTION is x = -1.5, because at that x-value, the y-value is at or below 0 #57) TEST MONDAY 4/7/08

8. AIM: HOW DO WE INVESTIGATE THE BEHAVIOR OF POLYNOMIAL INEQUALITIES? ***An alternate approach to solving polynomial inequalities.*** HW p. A73 #55, 61 8 Solving Rational Inequalities: Simplify, if necessary Procedure: HW p. A73 # 69, 70 Recall: FOR < 0: pos/neg = neg neg/pos = neg FOR > 0: pos/pos = pos neg/neg = pos Write as a single fraction. Write inequality in standard form (set equal to 0).

9. AIM: HOW DO WE INVESTIGATE THE BEHAVIOR OF POLYNOMIAL INEQUALITIES? ***An alternate approach to solving polynomial inequalities.*** HW p. A73 #55, 61 9 HW p. A73 # 69, 70

10. AIM: HOW DO WE INVESTIGATE THE BEHAVIOR OF POLYNOMIAL INEQUALITIES? ***An alternate approach to solving polynomial inequalities.*** HW p. A73 #55, 61 10 Solving Rational Inequalities using critical values and test intervals: NOTE THAT x = 5 IS NOT INCLUDED IN THE SOLUTION SET BECAUSE THE INEQUALITY IS UNDEFINED AT x = 5 HW p. A73 # 69, 70

11. AIM: HOW DO WE INVESTIGATE THE BEHAVIOR OF POLYNOMIAL INEQUALITIES? ***An alternate approach to solving polynomial inequalities.*** HW p. A73 #55, 61 11 Solving Rational Inequalities: CRITICAL VALUES: TEST INTERVALS: The curve is undefined at x = -1; check in original inequality. HW p. A73 # 69, 70