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Drawing Graphs of Implicit Functions

on the TI-89

To graph an implicit function, first press the Mode key key and switch "Graph..." to "5: 3D."

Now, you can press diamond key F1 key and type the function. The equation shown at right is from Exercise 29 on p. 139 of the Larsen text. Note:

  • You have to move all terms to the left side of the equation, so the equation (x2 + y2)2 = 4x2y must be converted to z1 = (x2 + y2)2 - 4x2y.
  • Be careful that you put an explicit multiplication symbol between variables! If you type "xy", the calculator will interpret it as a single variable named "xy" - if you mean "x times y", type "x" mult key "y."

Next, from the F1 window, select "9; Format."

From the "Style" menu, select "5: Implicit Plot."

Now, you can graph the function. Be warned, though - it takes a while! The calculator will keep you informed of progress as it calculates the plot. You can use the "F2 - Zoom" menu for standard zooming, and you can use the blue arrow keys to rotate the graph.

last update October 29, 2008 by JL Stanbrough