Transformations and Functions

Ideas for working with functions and transformations:
(The TI-83+ is the graphing calculator being referenced on this page.)

1. Supply students with an equation to enter into their graphing calculators.  Call this function the parent graph.

Ask students to perform transformations, or describe transformations, to the parent graph:
a.)  graph the function with a vertical stretch of factor 1/2 and a translation of 3 units to the left.
b.)  graph the function with a translation of 6 units to the right.
c.) describe the transformation that occurred if a new function's equation is

d.) describe the transformation that occurred if a new function's equation is

 

2. Provide students with a parent function, y = x2 -1, and a series of graphs that show transformations of this parent function.  Ask students to find equations for these transformations, OR ask students to match these graphs to formulas which you supply.
     
Possible formulas (not in matching order):
y = (x/2)2 - 1
y = 2 (x2 - 1)
y = (1/2)(x2 - 1)

 

3. Create a series of Transformation Cards to be used with functions.  This idea is similar to the activity presented in Math A, Shuffling Cards to Practice Transformations.  Detailed directions and additional ideas may be found on the Math A page.  The Math A page will open in a new window.

Transformation Cards:

Vertical
 stretch of a factor of 2

Translation of 3 units to the right

Translation
 of 4 units down

Horizontal stretch of a factor of 0.25
 

Create as many transformation cards as you have concepts that you wish to review.

Function Cards:
 

y = 3x + 2

y = x2 + 1

 y = - 2x -1

y = - x2 - 2
 

Create enough function cards so that each student (or group of students)
will be preparing unique answers.

 

 


Roberts