Defined Functions

You can plot a defined function of two variables in two different ways. Recall that you define a function such as

f (x, y) = $\displaystyle {\dfrac{{xy}}{{\left( x^{2}+y^{2}\right) ^{2}}}}$

by placing the insertion point in the expression and choosing New Definition from the Define submenu.

$\blacktriangleright$ To plot a defined function f of two variables

1.
Select the function name f or select the expression f (x, y).

2.
From the Plot 3D submenu, choose Rectangular.


$\blacktriangleright$ To add a defined function g of two variables to a 3D plot

1.
Select the function name g or select the expression g(x, y).

2.
Drag your selection onto the plot.


For the example that follows, define f (x, y) = ${\frac{{xy}}{{\left(
x^{2}+y^{2}\right) ^{2}}}}$ and g(x, y) = - 5. This example shows 3D rectangular plots of f (x, y) and of both f (x, y) and g(x, y), with Ranges - 1≤x≤1 and -1≤y≤1, and View Intervals -1≤x≤1, -1≤y≤1, and -5≤z≤5. The default View Intervals for z produces a plot that contains only a single vertical line. In the Plot Properties + Axes & View tabbed dialog, deactivate Default under View Intervals, and change the interval for z to get the plots shown in the example.

$\blacktriangleright$ Plot 3D + Rectangular

f (x, y)         Add g(x, y) for the second plot.

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