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Title: Transformations of a Function
Book Description: 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.
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.
Author: Mike Pepe
Suggested Use: If you know what the graph of y = f(x) looks like, then what does the graph of y = f(x-2) look like? And what aboyt the graph of y = f(x+2) or of y = f(3*x) ? If you had to stop for a moment to think about it, then you are like the rest of us. If you were unable to see "what to do" then this WorkBook is definitely for you. The WorkBook is full of experiments that will show you with many built-in examples
Number of Pages: 11
Animation: Yes
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