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Exploring the Witch of Agnesi

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This activity has students construct the graph of the Witch of Agnesi, and investigate both its asymptotes and inflection points. Fermat studied this function in the seventeenth century.

Mathematics: Students will construct the graph of the Witch of Agnesi and conjecture the asymptotes and inflection points of the function. Furthermore, students will algebraically derive the equation of the function using similar triangles and then formally compute the asymptotes and inflection points of the function.

Mathematical Thinking: Students will be asked to conjecture the basic shape of the function, and derive the graph’s equation.

Technology: This activity uses several Sketchpad commands such as: Create Axes, Circle by Center+Point, Plot Points, Ray, Color, Trace Point, and Action Button -» Animation.

The following sketch illustrates the Witch of Agnesi function.




The equation of "The Witch" is .




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Last modified on August 13, 2001.