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Polynomial and Rational Inequalities

Polynomial and Rational Inequalities. Lesson 4.6. 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

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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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