Dynamically-Generated Rational Function Examples

Discover characteristics of rational functions that are not possible with polynomial functions.

 Witch of Maria Agnesi The "witch" is a particular plane cubic curve. It is a bell-shaped curve with a horizontal asymptote. Witch of Maria Agnesi with a Hole Serpentine Serpent-shaped curve with horizontal asymptote Serpentine with Two Holes A Slant (Oblique) Asymptote On dividing the numerator by the denominator, the polynomial quotient is a linear function. That linear function is the slant asymptote. A Parabolic Asymptote On dividing the numerator by the denominator, the polynomial quotient is a quadratic function. That quadratic function is the parabolic asymptote. One Vertical Asymptote and a Horizontal Asymptote On dividing the numerator by the denominator, the polynomial quotient is a constant. That constant function is the horizontal asymptote. One Vertical Asymptote and a Slant (Oblique) Asymptote One Vertical Asymptote and a Parabolic Asymptote Use Smart Zooming with, say, Xmin=–3 and Xmax=3 and click the GraphAgain button to get a better sense of the parabolic asymptote. One Vertical Asymptote and a Cubic Asymptote Use Smart Zooming with, say, Xmin=–3 and Xmax=3 and click the GraphAgain button to get a better sense of the cubic asymptote. On dividing the numerator by the denominator, the polynomial quotient is a cubic function. That cubic function is the cubic asymptote. Two Vertical Asymptotes and a Horizontal Asymptote Two Vertical Asymptotes and a Slant (Oblique) Asymptote Two Vertical Asymptotes and a Parabolic Asymptote See How Color Coding Predicts "Hidden" Features Use Smart Zooming with, say, Xmin=–0.2 and Xmax=0.5 and click the GraphAgain button to reveal two more turning points.

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