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1.3transformations

# 1.3transformations - Section 1.6 Transformation of...

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Section 1.6 Transformation of Functions

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Graphs of Common Functions

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-4 -3 -2 -1 1 2 3 4 5 -4 -3 -2 -1 1 2 3 4 x y Reciprocal Function ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 Domain: - ,0 0, Range: - ,0 0, Decreasing on - ,0 0, Odd function and 1 ( ) f x x =
Vertical Shifts

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( 29 ( 29 ( 29 ( 29 Vertical Shifts Let be a function and be a positive real number. The graph of is the graph of shifted units vertically upward. The graph of is the graph of shifted f c y f x c y f x c y f x c y f x c = + = = - = units vertically downward.
Vertical Shifts

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Example Use the graph of f(x)=|x| to obtain g(x)=|x|-2 -4 -3 -2 -1 1 2 3 4 5 -4 -3 -2 -1 1 2 3 4 x y

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Horizontal Shifts
( 29 ( 29 ( 29 ( 29 Horizontal Shifts Let be a function and a positive real number. The graph of is the graph of shifted to the left units. The graph of is the graph of shifted to the f c y f x c y f x c y f x c y f x = + = = - = right units. c

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Horizontal Shifts
Example Use the graph of f(x)=x 2 to obtain g(x)=(x+1) 2 -4 -3 -2 -1 1 2 3 4 5 -4 -3 -2 -1 1 2 3 4 x y

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Combining Horizontal and Vertical Shifts
Example Use the graph of f(x)=x 2 to obtain g(x)=(x+1) 2 +2 -4 -3 -2 -1 1 2 3 4 5 -4 -3 -2 -1 1 2 3 4 x y

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Reflections of Graphs
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1.3transformations - Section 1.6 Transformation of...

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