# Exploring Function Transformations in 3D

## TEACHING TIP

Math Teachers: Students who study transformations of graphs of parent functions (linear, quadratic, cubic, absolute value, square root, etc...) in 2D CAN APPLY THE SAME TRANSFORMATIONS to graphs of "parent surface functions" in 3D! Here, we illustrate with the parent right-circular cone function, whose surface equation is . Note, in the 2D coordinate plane, if the same function transformations shown here were done of the graph of the basic linear function , we would get a slant segment whose length and inclination are the same as the slant height of the cone(s) shown in the screencast below.

## DEMO 2:

In this demo, we create surface models for these same 2 cones. Yet this time, one is placed on top of the other. How would we change these 2 surface equations if we decided to place the wider cone on top of the taller one instead?

## DEMO 3:

Notice here that these same two cones were shifted LEFT/RIGHT AND UP/DOWN. These surface graphs were also vertically stretched.