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Polynomial and Rational Inequalities

Learn how to solve polynomial and rational inequalities symbolically with step-by-step instructions and examples. Utilize boundary numbers, test values, and intervals to determine solutions. Includes exercises for practice.

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Polynomial and Rational Inequalities

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  1. Polynomial and Rational Inequalities Lesson 4.6

  2. Steps for Symbolic Solution • Write as an equation • Solve resulting equation for boundary numbers • Use boundary numbers to separate number line into disjoint intervals • Make a table of test values • One value from each interval • Use this to specify which intervals satisfy the original inequality

  3. ≤ 0 Example • Consider • Rewrite as an equation = 0 and graph • Determine zeros • Note and testintervals

  4. Numeric Solution • View table on calculator • Note intervals of xwhere the functiongoes above or(in this case)below zero

  5. Solving Rational Inequalities • Given an inequality involving a rational function, • As necessary rewrite • Solve p(x) = 0, q(x) = 0 • Solutions are boundary numbers • Use boundary numbers to separate number line into disjoint intervals • On intervals is always > 0 or < 0 • Use test values to solve original inequality

  6. boundary points Example • Solve • 2x = 0 when x = 0 • (x – 2) = 0 when x = 2 • Determine intervalswhich satisfyinequality • Note functionundefinedat x = 2

  7. Assignment • Lesson 4.6 • Page 309 • Exercises1 – 47 odd

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