1. 3.5 Polynomial and Rational Inequalities 1.Solve Polynomial Inequalities Algebraically and Graphically 2.Solve Rational Inequalities Algebraically and Graphically 1.Solve Polynomial Inequalities Algebraically and Graphically 2.Solve Rational Inequalities Algebraically and Graphically

2. Warm-up 1)Solve the Variation Problem: One’s Intelligence quotient, or IQ, varies directly as a person’s mental age and inversely as that person’s chronological age. A person with a mental age of 25 and chronological age of 20 has an IQ of 125. What is the chronological age of a person with a mental age of 40 and IQ of 80? 1)Solve the Variation Problem: One’s Intelligence quotient, or IQ, varies directly as a person’s mental age and inversely as that person’s chronological age. A person with a mental age of 25 and chronological age of 20 has an IQ of 125. What is the chronological age of a person with a mental age of 40 and IQ of 80?

3. (-1.5,0) (2,0) Solving Inequalities from the graph Solve the following using the graph.

4. 2. Solving Polynomial Inequalities algebraically Solve algebraically: Step 1: Rewrite as Step 2: Solve for boundary points, solve Step 3: Locate boundary points on number line, dividing into intervals. Step 4: Test points in each interval. Make a table. Step 5: Write down the intervals satisfying the problem from Step 1.

5. Solve the Polynomial Inequalities Interval Test Value Value of f Conclusion Interval Test Value Value of f Conclusion

6. Solve the Polynomial Inequalities Interval Test Value Value of f Conclusion Interval Test Value Value of f Conclusion

7. Solving Inequalities from the graph Solve the following using the graph.

8. Step 1: a) Get everything on the left side and zero on the other. b) Write as a single rational expression : or Solving Rational Inequalities What steps did we use to solve rational inequalities? Steps 2-5: Same as earlier

9. Solving Inequalities Solve the following inequality without graphing:

10. Solving Inequalities Solve the following inequality without graphing:

11. Practice Problem Solve the following inequality without graphing:

12. Application A ball is thrown upward with an initial velocity of 96 feet per second. The distance s (in feet) of the ball from the ground after t seconds is. a) When is the ball more than 112 feet above the ground?