3D graphs of two-variable functions — spin the surface with your mouse
Function z = f(x, y)
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Drag to rotate, wheel or pinch to zoom. The height of the surface is the value of z; the color shows the height too — from the lower color to the upper one.
📚 Theory: how to read a 3D graph
A function of two variables z = f(x, y) assigns one number z to every pair of numbers (x, y). If an ordinary graph y = f(x) is a line above the number line, the graph of a two-variable function is a surface above the plane: at every floor point (x, y) the surface is raised to height z.
Example: z = x² + y² is a “bowl”. At the center (0, 0) the height is zero, and the farther from the center, the higher the surface rises. And z = x² − y² is a “saddle”: along one axis the surface bends up, along the other — down.
Such surfaces describe terrain (height as a function of coordinates), the temperature of a hotplate (heat as a function of position), loudness in a room. Contour lines on a map are slices of such a surface by horizontal planes.
You can write: + − * / ^, parentheses, sin cos tan sqrt abs ln log exp, constants pi and e, variables x and y. Multiplication can be omitted: 2x, but between variables write it explicitly: x*y.