3_8 - in Step 3. The second row is the SIGNS of the f...

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Section 3.8: Polynomial and Rational Inequalities Instructor: Ms. Hoa Nguyen (nguyen@scs.fsu.edu) 1 Steps for Solving Polynomial and Rational Inequal- ities Step 1 : Write the inequality in either one of these forms: f ( x ) > 0, f ( x ) 0, f ( x ) < 0, f ( x ) 0. Step 2 : Find the zeros of f ( x ) if f is a polynomial. For a rational function f ( x ) = p ( x ) q ( x ) , ﬁnd the zeros of p ( x ) and the zeros of q ( x ). The zeros of p ( x ) are the zeros of f ( x ) , but the zeros of q ( x ) are the values where f is UNDEFINED . Step 3 : Order the zeros found in Step 2 (from least to greatest). Step 4 : Set up the table where: The ﬁrst row is the real number line separated into intervals by the ordered zeros

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Unformatted text preview: in Step 3. The second row is the SIGNS of the f values at the test points. For each interval, the test number is selected as some point in the interval. If the value of f is positive, then f ( x ) > 0 for all numbers x in the interval. If the value of f is negative, then f ( x ) < 0 for all numbers x in the interval. If the inequality has the equal sign (i.e., or ), then include the zeros of f . Important notation : [ a, b ) means the point a is included in the interval, but the point b is not. 1 2 Examples Example 4 2...
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This note was uploaded on 05/23/2011 for the course MAC 1147 taught by Professor Nuegyen during the Spring '11 term at FSU.

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3_8 - in Step 3. The second row is the SIGNS of the f...

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