If you're studying classes of functions and function transformations in 2D, YOU CAN build and model in 3D! [br][br]In 2D, consider the equation [math]x^2+y^2=4[/math]. It's graph is a circle with center (0,0) and radius = 2. [br]To see why, [url=https://www.geogebra.org/m/RCYvXnuR]check out this resource here[/url]. [br][br]Yet in this equation, if we replace y with z, this equation becomes [math]x^2+z^2=4[/math]. [br][br]If we solve explicitly for z, we get [math]z=\sqrt{4-x^2}[/math] (upper semicircle) and [math]z=-\sqrt{4-x^2}[/math] (lower semicircle).[br][b]In 3D, think of z as the new DEPENDENT VARIABLE. [/b][br][br]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). [br][br]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).[br] [br]Now if we add "0.3y" to both surfaces, what happens? [b][color=#ff00ff][i]Why do we get a slide? [/i][/color][/b]