If you're studying classes of functions and function transformations in 2D, YOU CAN build and model in 3D!
In 2D, consider the equation . It's graph is a circle with center (0,0) and radius = 2.
To see why, check out this resource here.
Yet in this equation, if we replace y with z, this equation becomes .
If we solve explicitly for z, we get (upper semicircle) and (lower semicircle).
In 3D, think of z as the new DEPENDENT VARIABLE.
If we graph these 2 surfaces in 3D, the value of y doesn't matter. Thus, these semicircles become infinitely long half-cylinders (see screencast below).
Here, if we study the relationship of z with respect to x (only) -- while ignoring y --, we have cross sections of planes (that are parallel to the xAxis) that are circles (formed from the upper and lower semicircles put together).
Now if we add "0.3y" to both surfaces, what happens? Why do we get a slide?