Transformations of Functions

Tansformations of Functions

This applet will help students discover how the graph of an equation can be transformed. It will develop cognitive skills in guessing the shape of a graph based on it's "parent" graph.

Click on sliders A, B, and C to transform the blue "Parent" graph to the red graph.

Instructions/Questions for Students:

Let's begin by manipulating the slider labeled "C".
1- What happens if C is bigger than 0?
2- What happens if C is less than 0?
Set C back to 0.

Let's now manipulate the slider labeled "B".
3- What happens if B is bigger than 0?
4- What happens if B is less than 0?
5- How would the equation represent these movements? Notice that in the equation you have in parenthesis (x-B).
Set B back to 0.

6- Guess: What does the graph of (x+3)²-3 look like compared to x²?

Move the sliders to verify your answer.

Let's now look at slider A.
7- What happens if A is bigger than 1?
8- What happens if A is less than 1 but bigger than 0?
9- What happens if A is equal to zero? Why?
10- What happens if A is less than zero?

Click on the check box for Point P to appear. P will trace itself as you move any slider. Move slider A.
11- What happens to P as you move A?

Right click on P, and select Trace Off. Click on the check box for Point P to disappear.

12- Guess: What does the graph of 2(x-3)²+2 look like compared to x²?
13- Guess: What does the graph of .5(x+1)²-1 look like compared to x²?
14- Guess: What does the graph of -2(x+2)²-4 look like compared to x²?

15- What do you think will happen to these rules of transformations if the power of the equation is changed?

Click on the Change Exponent Box to investigate further!

Bryan Stephenson, October 8, 2010, Created with GeoGebra