In
mathematics, we often use one function to define another. For example if we
start with the function f(x) = x^2 we can create a new function F by defining
F(x) = f(x) +3, so F(x) = x^2 +3. In words, F is the function that adds three
to the output of the function f. We refer to this new function F as a "transformation"
of the function f.
The
graphs of f and F are closely related . As you might expect, the graph of
F is just the graph of f shifted three units upward. What's important is that
this will be true in general. That is if we start with ANY function f and
then define the transformation F(x) = f(x) +3, the graph of F will always
be the graph of f shifted three units upward.
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For proper viewing, be sure to use Version 1.003 or later, dated Jan 13, 2002
Microworld: Transformations
of a Function
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the Hyperlink above to visit the Microworld.
Author:
Mike
Pepe
Topics: This book examines various standard transformations of functions and their associated graphs. In each case we will be interested in seeing how an algebraic transformation leads to the geometric transformation of the graph of f.
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