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3.5 Polynomial and Rational Inequalities

3.5 Polynomial and Rational Inequalities. Solve Polynomial Inequalities Algebraically and Graphically Solve Rational Inequalities Algebraically and Graphically. Warm-up. Solve the Variation Problem:

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3.5 Polynomial and Rational Inequalities

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

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

  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

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

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

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

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