Section 3.4 & 3.5 - Section 3.4 Graphing Rational...

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Unformatted text preview: Section 3.4 Graphing Rational Functions Analyzing the Graph of a Rational Function Step 1: Find the domain. Step 2: Locate the intercepts, if any. If the rational function is in lowest terms the xintercepts will occur when p(x) = 0, and the yintercept, if there is one, will be R(0). Step 3: Test for symmetry. If R is even then it has symmetry with respect to the yaxis if odd then it is symmetric with respect to the origin. Analyzing the Graph of a Rational Function Step 4: Write R in lowest terms, or carry out the division. The real zeros of the denominator will be vertical asymptotes. Step 5: Locate the horizontal and oblique asymptotes and determine the points, if any, at which the graph of R intersects these asymptotes. Analyzing the Graph of a Rational Function Step 6: Determine where the graph is above the xaxis and where it is below it. Use the zeros of the numerator and denominator into intervals then test the intervals. Step 7: Graph the asymptotes, if any. Plot the intercepts, the points where the graph crosses the asymptotes. Use the information to connect the points and graph R. Section 3.5 Polynomial and Rational Inequalities Steps for Solving Polynomial and Rational Inequalities Step 1: Write the inequality so that a polynomial or rational expression f is on the left side and zero is on the right side. For rational expressions make sure the left side is written as a single quotient. Step 2: Determine when the left equals zero and, if the expression is rational, when it is undefined. Steps for Solving Polynomial and Rational Inequalities Step 3: Use the numbers found in step 2 to separate the real line into intervals. Step 4: Select a number in each interval to evaluate f at to determine if f is positive or negative on the interval. Step 4: Take the union of the appropriate intervals, and if the inequality is not strict include the solutions of f(x) = 0. ...
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This note was uploaded on 08/26/2009 for the course MATH 125 taught by Professor Staff during the Fall '08 term at Southern Illinois University Edwardsville.

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