# Exploring Function Transformations in 3D

- Author:
- Tim Brzezinski

- Topic:
- Functions, Reflection

## 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

## TEACHING TIP DEMO:

## 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 2

## DEMO 3:

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