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2.6 Rational Functions

2.6 Rational Functions. Steps for Graphing guidelines. 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

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2.6 Rational Functions

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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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