Thread:HMcCoy/@comment-28838092-20141215195834/@comment-24808864-20141215202422

A graph and a function are two different things. Independent and dependent variables are words used about functions...not graphs.

However, all functions can be represented by graphs, but not all graphs are functions (they need to pass a "vertical line test" or some other appropriate condition).

Regarding the z-variable: the z-variable will (most of the time) be a dependent variable, but the y-variable in 3D cases may be dependent or independent.

Example of x,y independent, z dependent:  $$z=f(x,y)=x^2+y^2 $$ which is a parabolic cup

Example of x independent, y,z dependent: $$(y,z)=f(x)=(x^2,2x) $$

Notice in the first example, you put in x and y, and the function yields a z. In the second example you put in x, and the function yields an ordered pair (y,z) with two outputs that depend on the input x.

After Calculus AB and Calculus BC are mastered, Multivariable Calculus or Vector Calculus is where you will study the calculus on higher dimensions such as 3D (and beyond)!