Gallery of Dynamically-Generated Interactive 3D Function Graphs

Note: the scale for each axis is the number line that is parallel to the axis.

 Plane in 3D: z = 1-x/2-y/3 Elliptic Paraboloid: z = x^2+2y^2  Note that the cross-sections parallel to the z-axis are parabolas, while the cross sections parallel to the x-y plane are ellipses. Compare this surface plot to the 3D Level Surface plot of the same elliptic paraboloid that places bounds on z as well as x and y. In this graph, the "invisible rectangular box" containing the graph cuts the four vertical sides into parabolas. Monkey Saddle: z = x^3-3x*y^2  So named because a monkey sitting in the saddle would have a place for its tail. (Rotate the graph so that the x-axis is facing left, the z-axis is facing up, and the y-axis is pointing at you. Visualize the monkey sitting in the saddle, facing left, with his tail resting down on the right. Note that while the x-axis is facing left, the scale for the x-axis is parallel to the x-axis at the top of the 3D graph.) Cyclical Function: z = sin(x^2+y^2)  The circular-shaped mound in the center is repeated continuously with larger radii, so that you have a succession of concectric mounds centered at the origin. Hemisphere: z = (4-x^2-y^2)^(1/2)  The top half of a sphere. z = e^(-x)cos(y) z = (3-x^2+4y^2)e^(1-x^2-y^2) Another Cyclical Function: z = sin(sin((x*y)) z =log(1+x^2+y^2)

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