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Section 4.1 – Rational Functions and Asymptotes

Section 4.1 – Rational Functions and Asymptotes. Graphing and Analyzing Rational Functions. Domain Vertical Asymptotes (x = ) Horizontal Asymptotes (y = ) Holes (x, y) Intercepts Graph. Find the equations of the horizontal asymptotes of:. Domain: . Vertical Asymptotes:.

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Section 4.1 – Rational Functions and Asymptotes

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  1. Section 4.1 – Rational Functions and Asymptotes

  2. Graphing and Analyzing Rational Functions • Domain • Vertical Asymptotes (x = ) • Horizontal Asymptotes (y = ) • Holes (x, y) • Intercepts • Graph

  3. Find the equations of the horizontal asymptotes of:

  4. Domain: Vertical Asymptotes: Horizontal Asymptotes: Holes: Intercepts:

  5. Domain: Vertical Asymptotes: Horizontal Asymptotes: Holes: Intercepts:

  6. Domain: Vertical Asymptotes: Horizontal Asymptotes: Holes: Intercepts:

  7. Domain: Vertical Asymptotes: Horizontal Asymptotes: Holes: Intercepts:

  8. Extension: The graph contains an hole at x = -3 Note: Cancelled and eliminated Extension: The graph contains an asymptote at x = 3 Note: not eliminated

  9. Domain: Vertical Asymptotes: Horizontal Asymptotes: Holes: Intercepts:

  10. Extension: The graph contains a hole at x = -2 Note: cancelled and eliminated

  11. Domain: Vertical Asymptotes: Horizontal Asymptotes: Holes: Intercepts:

  12. Graph the rational function which has the following characteristics Vert Asymp at x = 1, x = -3 Horz Asymp at y = 1 Intercepts (-2, 0), (3, 0), (0, 2) Passes through (-5, 2)

  13. Graph the rational function which has the following characteristics Vert Asymp at x = 1, x = -1 Horz Asymp at y = 0 Intercepts (0, 0) Passes through (-0.7, 1), (0.7, -1), (-2, -0.5), (2, 0.5)

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