Transformations of Functions

Transformations of Functions - 2.5 Transformations of...

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2.5 - Transformations of Graphs Every College Algebra student must be able to identify the following six parent graphs. f ( x ) = x f ( x ) = x 2 x y x y Domain = ________________________ Domain = ________________________ Range = __________________________ Range = __________________________ f ( x ) = x 3 f ( x ) = | x | x y x y Domain = ________________________ Domain = ________________________ Range = __________________________ Range = __________________________ f ( x ) = x f ( x ) = 3 x x y x y Domain = ________________________ Domain = ________________________ Range = __________________________ Range = __________________________
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Vertical Translations If f is a function and k is a positive constant, then the graph of œ y = f ( x ) + k is the graph of y = f ( x ) shifted up vertically k units. œ y = f ( x ) - k is the graph of y = f ( x ) shifted down vertically k units. Examples: The graph of f ( x ) = x 3 is given below. Sketch the graph of g ( x ) = x 3 - 5. x -8 -6 -4 -2 2 y 8 6 4 2 -2 -4 -6 -8 4 6 8 The graph ofa function f is given below. Sketch the graph of y = f ( x ) + 3. x -8 -6 -4 -2 2 y 8 6 4 2 -2 -4 -6 -8 f 4 6 8
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HorizontalTranslations If f is a function and h is a positive constant, then the graph of œ y = f ( x + h ) is the graph of y = f ( x ) shifted left horizontally h units. œ y = f ( x - h ) is the graph of y = f ( x ) shifted right horizontally h units.
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