3.5 Polynomial and Rational Inequalities

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Presentation transcript:

3.5 Polynomial and Rational Inequalities

Solving Equations Let’s review solving the following equation: (-1.5,0) (2,0) *A polynomial function can only change signs at its zeros (x-ints).*

Solving Inequalities Solve the following inequality without graphing:

Solving Polynomial Inequalities What steps did we use to solve ? 1) Get everything on the left side to set equal to zero. 2) Find the zeros of f (x) by factoring. 3) Use zeros to separate real number line into test intervals. 4) Pick value from each test interval to evaluate sign of f (x). 5) Write out solution region in interval notation.

Solving Inequalities Solve the following inequality without graphing:

Solving Inequalities Solve the following inequalities without graphing: 1) 2)

Solving Rational Equations Let’s review solving the following equation: (-1.25,0) *A rational function can change signs at its zeros (x-ints) AND where f is undefined.*

Solving Inequalities Solve the following inequality without graphing:

Solving Rational Inequalities What steps did we use to solve rational inequalities? 1) Get everything on the left side and zero on the other. 2) Find the zeros AND where f (x) DNE by finding common denominator. 3) Use these to separate real number line into test intervals. 4) Pick value from each test interval to evaluate sign of f (x). 5) Write out solution region in interval notation.

3.5 Polynomial and Rational Inequalities Homework #3: Page 217 #11, 17, 23, 33 – 37 Odd, 43