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Rational Functions

Rational Functions. Mary Johnson CTSE 5040/6040 July 22, 2010. Objectives. Graphing rational functions – including horizontal and vertical asymptotes, and holes Solving rational equations and inequalities ( http://www.team-math.net ). Overview of Unit. The Breaking Point Experiment

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Rational Functions

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  1. Rational Functions Mary Johnson CTSE 5040/6040 July 22, 2010

  2. Objectives • Graphing rational functions – including horizontal and vertical asymptotes, and holes • Solving rational equations and inequalities (http://www.team-math.net)

  3. Overview of Unit • The Breaking Point Experiment • Characteristics of Rational Functions • Light It Up http://illuminations.nctm.org/LessonDetail.aspx?id=L606 • Transformations • Solving Rational Equations and Inequalities • Excel • CAS • Graphing Calculators • Online Activities Activities Technology

  4. Definition • A rational function is a ratio of two polynomials where the denominator is not identically zero

  5. Typical Treatment of Horizontal Asymptotes The rule for finding a horizontal asymptotedepends on the degree of the numerator, m, and denominator, n. • If m>n, then there is no horizontal asymptote. • If m<n, then the horizontal asymptote is at the x–axis. • If m=n, then you must compare the coefficients in front of the terms with the highest power. The horizontal asymptote is the coefficient of the highest power of the numerator divided by the coefficient of the highest power of the denominator. (http://www.algebralab.org/lessons/lesson.aspx?file=algebra_rational_graphing.xml)

  6. http://www.wolframalpha.com/ y=(3x^2+2x-3)/(x^2+x-2) y=(x^4-4x^2+x^3-4x)/(x^2-1)

  7. Equations Graph

  8. Equations Graph

  9. Impact of Technology • Without technology, no more than a superficial treatment of rational functions is possible. • CAS is especially useful here for factoring expressions and dividing to rewrite them as a mixed number. • Technology enables focus on the concepts not the computation.

  10. References • http://www.wolframalpha.com • http://www.algebralab.org/lessons/lesson.aspx?file=algebra_rational_graphing.xml • http://illuminations.nctm.org/LessonDetail.aspx?id=L606 • http://www.team-math.net/

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