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Comprehensive Steps for Graphing Rational Functions and Analyzing Asymptotes

Discover a step-by-step guide to graphing rational functions, including methods to find y-intercepts and x-intercepts. Learn how to determine the domain of the function, identify vertical and horizontal asymptotes, and decide if slant asymptotes exist. Understand the relationship between the degrees of the numerator and denominator when analyzing behavior at infinity. This guide also includes examples with specific rational functions, making it an essential resource for mastering graphing and understanding rational functions.

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Comprehensive Steps for Graphing Rational Functions and Analyzing Asymptotes

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  1. 2.6 Rational Functions Steps for Graphing guidelines.

  2. y-int. ( , ) 0 x-int. ( , ) none let x = 0 to find y-int. Domain: let y = 0 to find x-int.(s) where is g(x) undefined Asymptote(s) if x is undefined at a number, there is a vertical asymptote at that number. V.A. @ x = 2 Deg. of N < Deg. of D Compare the exponents. Do we have a horizontal at y = 0, a horz. at y = a/b, or a slant asymptote? is horz. asymptote

  3. x = 2 y = 0

  4. none y-int. ( , ) x = 0 x-int. ( , ) Domain: y = 2 Asymptote(s) V.A. @ x = 0 H.A.

  5. y-int. ( , ) 0 0 x = -1 x = 2 x-int. ( , ) 0 0 Domain: (x-2)(x+1) Asymptote(s) V.A. @ x = -1 x = 2 H.A. y = 0 b/c N < D

  6. y-int. ( , ) 0 2 Slant asymptotes x = 1 (x-2)(x+1) x-int. ( , ) ( , ) 2 0 -1 0 Domain: Asymptote(s) V.A. x = 1 Slant asym. y = x y = x

  7. (x-3)(x+3) y-int. ( , ) x-int. ( , ) ( , ) 3 0 -3 0 (x-2)(x+2) Domain: Asymptote(s) V.A. x = -2 x = 2 H.A.

  8. y-int. ( , ) 0 -1 x-int. ( , ) 1 0 Domain: Asymptote(s) V.A. x = -1 H.A.

  9. y-int. ( , ) x-int. ( , ) ( , ) Domain: Asymptote(s)

  10. y-int. ( , ) x-int. ( , ) ( , ) Domain: Asymptote(s)

  11. y-int. ( , ) x-int. ( , ) ( , ) Domain: Asymptote(s)

  12. y-int. ( , ) x-int. ( , ) ( , ) Domain: Asymptote(s)

  13. y-int. ( , ) x-int. ( , ) ( , ) Domain: Asymptote(s)

  14. y-int. ( , ) x-int. ( , ) ( , ) Domain: Asymptote(s)

  15. y-int. ( , ) x-int. ( , ) ( , ) Domain: Asymptote(s)

  16. y-int. ( , ) x-int. ( , ) ( , ) Domain: Asymptote(s)

  17. y-int. ( , ) x-int. ( , ) ( , ) Domain: Asymptote(s)

  18. y-int. ( , ) x-int. ( , ) ( , ) Domain: Asymptote(s)

  19. y-int. ( , ) x-int. ( , ) ( , ) Domain: Asymptote(s)

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