When you are done with this
section, you will be able to do the following:
Describe how a graph has been changed from the original using common transformations
Sketch the graph of a function using the common graphs and transformations
Write the equation of a function using common graphs and transformations
For this class, we will mostly focus on
vertical and horizontal shifts, reflections over the x-axis and
y-axis, and vertical stretching and shrinking.
Vertical and Horizontal shifts of
Graphs of Functions
On-line Notes:
Additional Vertical and Horizontal shifts of Graphs of Functions On-line Resources:
The Shifter (java applet lets you explore what different numbers do to a graph)
Shifting, Flipping, Stretching, and Compressing Basic Shapes
Purplemath - Your Algebra Resource: Function Transformations I
Purplemath - Your Algebra Resource: Function Transformations II
Purplemath - Your Algebra Resource: Finding formulas from the graphs
Purplemath -
Your Algebra Resource:
Function Transformation Quiz
Additional Reflections of Graphs of Functions On-line
Resources:
Shifting, Flipping, Stretching, and Compressing Basic Shapes
Purplemath - Your Algebra Resource: Function Transformations I
Purplemath - Your Algebra Resource: Function Transformations II
Purplemath - Your Algebra Resource: Finding formulas from the graphs
Purplemath - Your Algebra Resource: Function Transformation Quiz
Additional Vertical Stretching and
Shrinking of
Graphs of Functions On-line Resources:
Shifting, Flipping, Stretching, and Compressing Basic Shapes
Purplemath - Your Algebra Resource: Function Transformations I
Purplemath - Your Algebra Resource: Function Transformations II
Purplemath - Your Algebra Resource: Finding formulas from the graphs
6
Basic Functions
On-line Notes:
Additional 6 Basic Functions On-line Resources:
Transformation of Functions
Homework:
Movement related to the x variable (horizontally) requires that the change be made to the x before the rest of the function is done (such as before squaring) (i.e.: f(x + c) or f(cx)).
Movement related to the y variable (vertically) requires that the change be made to the output of the function (i.e.: f(x) + c or cf(x)).
When trying to figure out
a new
equation for a graph, focus on one obvious point and find out what
happened to it. If there is another point, check your hypothesis
on that point.
Keep in mind that up and
down movement
is makes sense as + and - respectively. Left and right movement
for most people seems backwards + and - respectively.
Homework examples:
also-recommended Homework examples:
Example 3: similar to problem 5 in also-recommended problems
Keep in mind that it is recommended that you also complete all the problems in the set called
"also recommended" with the same number as the Transformation of Functions Homework. There are many different ways to ask the same questions. This will allow you to see additional problems that are related to this topic.