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Rational Expressions, Vertical Asymptotes, and Holes

Rational Expressions, Vertical Asymptotes, and Holes. Rational Expression. It is the quotient of two polynomials. A rational function is a function defined by a rational expression. Examples:. Not Rational:. Find the domain:. Graph it:. Find the domain:. Graph it:. Find the domain:.

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Rational Expressions, Vertical Asymptotes, and Holes

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  1. Rational Expressions, Vertical Asymptotes, and Holes

  2. Rational Expression • It is the quotient of two polynomials. • A rational function is a function defined by a rational expression. Examples: Not Rational:

  3. Find the domain: Graph it:

  4. Find the domain: Graph it:

  5. Find the domain: Graph it:

  6. Find the domain: Graph it:

  7. Vertical Asymptote • If x – a is a factor of the denominator of a rational function but not a factor of the numerator, then x = a is a vertical asymptote of the graph of the function.

  8. Find the domain: Graph it using the graphing calculator. What do you see?

  9. Find the domain: Graph it using the graphing calculator. What do you see?

  10. Hole (in the graph) • If x – b is a factor of both the numerator and denominator of a rational function, then there is a hole in the graph of the function where x = b, unless x = b is a vertical asymptote. • The exact point of the hole can be found by plugging b into the function after it has been simplified.

  11. Find the domain and identify vertical asymptotes & holes.

  12. Find the domain and identify vertical asymptotes & holes.

  13. Find the domain and identify vertical asymptotes & holes.

  14. Find the domain and identify vertical asymptotes & holes.

  15. Find the domain and identify vertical asymptotes & holes.

  16. Find the domain and identify vertical asymptotes & holes.

  17. Find the domain and identify vertical asymptotes & holes.

  18. Find the domain and identify vertical asymptotes & holes.

  19. Horizontal Asymptotes & Graphing

  20. Horizontal Asymptotes • Degree of numerator = Degree of denominator • Degree of numerator < Degree of denominator • Degree of numerator > Degree of denominator Horizontal Asymptote: Horizontal Asymptote: Horizontal Asymptote:

  21. Find all asymptotes & holes & then graph:

  22. Find all asymptotes & holes & then graph:

  23. Find all asymptotes & holes & then graph:

  24. Find all asymptotes & holes & then graph:

  25. Find all asymptotes & holes & then graph:

  26. Find all asymptotes & holes & then graph:

  27. Find all asymptotes & holes & then graph:

  28. Find all asymptotes & holes & then graph:

  29. Find all asymptotes & holes & then graph:

  30. Find all asymptotes & holes & then graph:

  31. Find all asymptotes & holes & then graph:

  32. Find all asymptotes & holes & then graph:

  33. Find all asymptotes & holes & then graph:

  34. Find all asymptotes & holes & then graph:

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