mac1147_lecture17_1_c

mac1147_lecture17_1_c - L17 Rational Inequalities Zeros of...

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182 L17 Rational Inequalities; Zeros of a Polynomial Function S olving Rational Inequalities 1. Get all terms on the left side of the inequality with a 0 on the right side and simplify the left-hand side into a single fraction. Write the domain . Reduce the fraction. 2. Find all real zeros of the numerator and denominator . Determine their multiplicities. 3. Divide a real line into intervals using the zeros found in Step 2 and the numbers that are not in the domain . Label an endpoint as if it is to be included in the answer and label it as D if it is not. Note: Zeros of the denominator are never included! Zeros of the numerator which are in the domain are included if and only if the inequality is non strict ( , ). 4. Use the end behavior of the polynomials in the numerator and denominator to find the sign of the fraction on the right-most interval (when x →+∞ ). 5. Set the signs on each other interval by moving from the right to the left and changing/not changing the sign depending on multiplicity.
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mac1147_lecture17_1_c - L17 Rational Inequalities Zeros of...

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