Polynomial and Rational Inequalities

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Presentation transcript:

Polynomial and Rational Inequalities Objectives: Solve polynomial inequalities Solve rational inequalities

Procedure for solving Polynomial Inequalities: 1 Procedure for solving Polynomial Inequalities: 1. Express the inequality in the form where is a polynomial function 2. Solve the equation . Factor to find the real solutions called the boundary points or critical points 3. Locate these boundary points or critical points on a number line, thereby dividing the number line into intervals. Use open dots if the inequality is less than or greater than and closed dots if the inequality is less than or equal to or greater than or equal to. 4. Choose one representative number, called a test value, within each interval and evaluate at that number and shade appropriately. a) If the value of is positive, then for all numbers, x , in the interval b) If the value of is negative, then for all numbers, x, in the interval 5. Write the solution set in interval notation, selecting the interval or intervals that satisfy the given inequality

EX: Solve the inequality 2. 1. EX: Solve the inequality 2.

EX: Solve the inequality 4. 3. EX: Solve the inequality 4.

Procedure for Solving Rational Inequalities: 1 Procedure for Solving Rational Inequalities: 1. Change the inequality to an equality 2. Solve the equality to find the critical points 3. Plot the critical points on a number line using the open dots or closed dots 4. Set the denominator(s) equal to zero and solve to find more critical points 5. Plot the denominator critical points on a number line as open dots 6. Test a point in each interval determined by the critical points and shade appropriately 7. Write your answer in interval notation

EX: Solve each inequality 6. 5. EX: Solve each inequality 6.

EX: Solve each inequality 8. 7. EX: Solve each inequality 8.