mac1105_lecture17_1

mac1105_lecture17_1 - L17 Graphing Rational Functions;...

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179 L17 Graphing Rational Functions; Rational Inequalities Graphing Rational Functions : 1. Factor both the numerator and denominator. 2. Write the domain. 3. Reduce the fraction to lowest terms, if possible. 4. Give the vertical asymptotes and holes. 5. Find the x -intercept(s) and y -intercept. 6. Find the horizontal or oblique asymptote, if any. 7. Determine if the graph crosses its horizontal or oblique asymptote. 8. Test for symmetry. 9. Plot all asymptotes, holes, intercepts, and points of crossing of horizontal/oblique asymptote. 10. Using the end behavior and multiplicities of zeroes of both the numerator and denominator , determine the sign of the function on each interval between the intercepts/asymptotes. 11. Plot a few more points where it is needed. 12. Graph the function.
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180 Example : Graph the rational function 32 2 232 () 2 x xx Rx x x +− = Domain: Hole(s): VA(s): x -intercept(s): y -intercept: Horizontal or Oblique Asymptote:
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181 Crossing of the horizontal or oblique asymptote: Symmetry:
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182 Example : Construct a rational function from its graph.
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mac1105_lecture17_1 - L17 Graphing Rational Functions;...

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