Class_Notes_2.5 - for each basic function, a few examples...

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Section 2.5 Class Notes Graphing Techniques: Transformations Guiding Problem 1 On the same set of axes, draw each of the following functions: ( 29 2 2 2 ( ) , ( ) 3, ( ) 3 f x x g x x h x x = = + = - , ( 29 2 2 ( ) 3 , ( ) 3 m x x n x x = = Describe how each of the graphs of g , h , m , and n relates to the graph of f . (You should write four descriptive comparisons.) Big Picture In this section, we start looking at how the basic functions in your library of functions can be used to generate whole families of functions via transformations. Each family member is characterized by a “gene structure” that helps describe how that individual differs from the rest of the members of that same family. Basic Functions Family of Functions Identity Function ( ) f x x = Linear Functions ( ) ( ) f x a x b c = - + Square Function 2 ( ) f x x = Quadratic Functions 2 ( ) ( ) f x a x b c = - + Cubic Function 3 ( ) f x x = (Some) Cubic Functions 3 ( ) ( ) f x a x b c = - + In the section of your Math 19 binder titled “Encyclopedia of Functions”, it would be a good idea to include
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Unformatted text preview: for each basic function, a few examples of that functions relatives via transformations along with their graphs. Extra Practice Problems Each function below is a modification of one of the basic functions in your library of functions. For each, give the corresponding basic function and describe how you expect the graph of the function below will appear, relative to the graph of the basic function. Sketch the graph of each function below. ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 2 3 2 2 3 1 2 2 3 5 2 2 1 3 1 2 2 1 a f x x b f x x c f x x d f x x e f x x f f x x g f x h f x x i f x x j f x x x =-= + = + =-= = = -=-=-+ = --+ Answers:...
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This note was uploaded on 09/08/2010 for the course MATH 201A at San Jose State University .

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Class_Notes_2.5 - for each basic function, a few examples...

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