Transformations of a Function

© 2002, Michael Pepe
In mathematics we often use one function to define another. For example if we start with the function f(x) = x2 we can create a new function F by defining F(x) = f(x) +3, so F(x) = x2 +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 (see below). As you might expect, the graph of F (in red) is just the graph of f (in blue) 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. The microworld below will allow you to explore 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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