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Vertical

Sec 4.4: Curve Sketching. Horizontal. Asymptotes. Vertical. 1)Vertical Asymptotes 2) Horizontal Asymptotes 3) Slant Asymptotes. Slant or Oblique. called a slant asymptote because the vertical distance between the curve and the line approaches 0.

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Vertical

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  1. Sec 4.4: Curve Sketching Horizontal Asymptotes Vertical 1)Vertical Asymptotes 2) Horizontal Asymptotes 3) Slant Asymptotes Slant or Oblique called a slant asymptote because the vertical distance between the curve and the line approaches 0. For rational functions, slant asymptotes occur when the degree of the numerator is one more than the degree of the denominator. In such a case the equation of the slant asymptote can be found by long division as in the following

  2. Sec 4.4: Curve Sketching Slant or Oblique called a slant asymptote because the vertical distance between the curve and the line approaches 0 For rational functions, slant asymptotes occur when the degree of the numerator is one more than the degree of the denominator. In such a case the equation of the slant asymptote can be found by long division as in the following

  3. Sec 4.4: Curve Sketching Asymptotes 1)Vertical Asymptotes 2) Horizontal Asymptotes 3) Slant Asymptotes Horizontal Special Case: (Rational function) Horizontal or Slant

  4. Sec 4.4: Curve Sketching F091

  5. Sec 4.4: Curve Sketching F101

  6. Sec 4.4: Curve Sketching F081

  7. Sec 4.4: Curve Sketching F092

  8. Sec 4.4: Curve Sketching Slant or Oblique called a slant asymptote because the vertical distance between the curve and the line approaches 0 For rational functions, slant asymptotes occur when the degree of the numerator is one more than the degree of the denominator. In such a case the equation of the slant asymptote can be found by long division as in the following

  9. Sec 4.4: Curve Sketching F101

  10. Sec 4.4: Curve Sketching SKETCHING A RATIONAL FUNCTION • Intercepts • Asymptotes

  11. Sec 4.4: Curve Sketching GUIDELINES FOR SKETCHING A CURVE • Domain • Intercepts • Symmetry • Asymptotes • Intervals of Increase or Decrease • Local Maximum and Minimum Values • Concavity and Points of Inflection • Sketch the Curve Symmetry symmetric about the y-axis symmetric about the origin

  12. Sec 4.4: Curve Sketching Example • Domain • Intercepts • Symmetry • Asymptotes • Intervals of Increase or Decrease • Local Maximum and Minimum Values • Concavity and Points of Inflection • Sketch the Curve • Domain: R-{1,-1} • Intercepts : x=0 • Symmetry: y-axis • Asymptotes: V:x=1,-1 H:y=2 • Intervals of Increase or Decrease: inc (-inf,-1) and (-1,0) dec (0,1) and (1,-inf) • Local Maximum and Minimum Values: max at (0,0) • Concavity and Points of Inflection down in (-1,1) UP in (-inf,-1) and (1,inf) • Sketch the Curve

  13. Sec 4.4: Curve Sketching F081

  14. Sec 4.4: Curve Sketching • Easy to sketch: • Study the limit at inf

  15. Sec 4.4: Curve Sketching • Study the limit at inf

  16. Sec 4.4: Curve Sketching • Study the limit at inf

  17. Sec 4.4: Curve Sketching F083

  18. Sec 4.4: Curve Sketching F091

  19. Sec 4.4: Curve Sketching F091

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