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Witch
of Maria Agnesi
The "witch" is a particular plane cubic curve. It is a bell-shaped
curve with a horizontal asymptote. |
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Witch
of Maria Agnesi with a Hole
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Serpentine
Serpent-shaped curve with horizontal asymptote |
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Serpentine
with Two Holes
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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. |
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A
Parabolic Asymptote
On dividing the numerator by the denominator, the polynomial
quotient is a quadratic function. That quadratic function is
the parabolic asymptote. |
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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. |
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One
Vertical Asymptote and a Slant (Oblique) Asymptote
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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. |
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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. |
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Two
Vertical Asymptotes and a Horizontal Asymptote
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Two
Vertical Asymptotes and a Slant (Oblique) Asymptote
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Two
Vertical Asymptotes and a Parabolic Asymptote
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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. |
