5.4 Polynomial&Rational Inequalities

5.4 Polynomial&Rational Inequalities - in that...

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5.4: Polynomial & Rational Inequalities Steps for solving polynomial and rational inequalities: [1] Set the inequality equal to zero; rational inequalities should be written as a single quotient. [2] Find the numbers at which the expression f is equal to zero and, if rational, the numbers at which it is undefined; these are called critical points. [3] Use the numbers found in step 2 to separate the real number line into intervals. [4] Evaluate f for a number in each of the intervals: [a] If the value of f is positive, then f(x) > 0 for all numbers
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Unformatted text preview: in that interval; [b] If the value of f is negative, then f(x) < 0 for all numbers in that interval. Solve each of the following: 1. (x – 8)(x + 3) > 0 2. x 2- 3x ≤ 0 1. 2. Result Result 3. 8x 2 < 6 –13X 4. 2(2x 2 – 6x) > -9 3. 4. Result Result 5. 4x 2 + 49 < 28x 6. x 4 ≤ 8x 5. 6. Result Result 7. 2 2 15 1 x x x--+ 8. 18 9 x x + ≤ Zeros: Asymptote: 7. 8. Result Result 9. 6 2 2 6 x x-≤-Zeros: Asymptote: 9. Result 10. 2 5 1 1 1 x x x x + + < +-Zeros: Asymptotes: 10. Result...
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