## Level surfaces

Scroll down to the bottom to view the interactive graph.

Level surface are basically the same as level curves in principle, except that the domain of $$f(x,y,z)$$ is in 3D-space. Therefore, the set $$f(x,y,z) = k$$ describes a surface in 3D-space rather than a curve in 2D-space.

The following diagram shows the level surfaces $f(x,y,z) = x^2 + y^2 - x^2 = k$ for various $$k$$ values. The level surfaces are hyperbolas of one or two sheets, depending on the values of $$k$$. Nevertheless, the value of $$f(x,y,z)$$ stays the same at each points on a level surface.

To view the interactive graph:

1. Make sure you have the latest version of Java 7 installed in your computer. Tablets and smartphones are not supported.