9.3 Intro to Rational Functions

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  • Kristen-
    Cool presentation. You just gave me a great idea to do with my students around rational functions. I'm a high school teacher at an international 1 to 1 laptop school in Taiwan. I am always looking for cool ways to incorporate the technology into my math classroom. You're presentation gave me the idea to have the students create digital stories about rational functions.
    Thank you for sharing.
    Chrisanne Roseleip
    http://twitter.com/ roseleipc
    Taipei, Taiwan
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9.3 Intro to Rational Functions

  1. 1. 9.3 Rational Functions and Their Graphs
  2. 2. A rational function is. . .
  3. 3. Examples of Rational Functions Where does the denominator = 0?
  4. 4. Examples of Rational Functions Where does the denominator = 0?
  5. 5. Examples of Rational Functions Where does the denominator = 0?
  6. 6. A point of discontinuity occurs when. . . It causes or in the graph.
  7. 7. Example 1. Find the points of discontinuity. a. 1x2x 1 y 2 ++ = b. 1x 1x y 2 + +− =
  8. 8. If a number is a solution to only the denominator of a rational function, then it creates an __________________ in the function. ex. )2x)(1x( 1x y +− + =
  9. 9. If a number is a solution to both the numerator and denominator of a rational function, then it creates a _____________ in the function. ex. )1x)(2x( 2x y −− − =
  10. 10. Example 2. Describe the vertical asymptotes and holes for the graph of each rational function. a. b.)3x)(2x( 1x y −− + = 2x )1x)(2x( y − −− =
  11. 11. c. d. )4x)(3x)(3x( )4x)(3x( y +−− +− = 1x 1x y 2 + − =
  12. 12. Horizontal Asymptotes A horizontal asymptote depends on the biggest power of the numerator and denominator. 1. If n > d, 2. If n < d, 3. If n = d,
  13. 13. Example 3. Find the horizontal asymptotes of each function. a. b. c. 1x 6x2 y − +− = 2 x 1 y = x5 x2x y 3 + =
  14. 14. Example 4. Sketch the graph of Points of discontinuity: Holes: Vertical Asymptotes: Horizontal Asymptotes: )4x)(3x( 2x y −+ + =
  15. 15. Assignment:

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