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Section 1.6 Transformation of Functions
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Graphs of Common Functions
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Reciprocal Function
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Vertical Shifts
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Vertical Shifts
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Example Use the graph of f(x)=|x| to obtain g(x)=|x|-2
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Horizontal Shifts
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Horizontal Shifts
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Example Use the graph of f(x)=x2 to obtain g(x)=(x+1)2
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Combining Horizontal and Vertical Shifts
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Example Use the graph of f(x)=x2 to obtain g(x)=(x+1)2+2
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Reflections of Graphs
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Reflections about the x-axis
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Example Use the graph of f(x)=x3 to obtain the graph of g(x)= (-x)3.
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Example
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Vertical Stretching and Shrinking
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Vertically Shrinking
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Vertically Stretching
Graph of f(x)=x3 Graph of g(x)=3x3 This is vertical stretching – each y coordinate is multiplied by 3 to stretch the graph.
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Example Use the graph of f(x)=|x| to graph g(x)= 2|x|
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Horizontal Stretching and Shrinking
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Horizontal Shrinking
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Horizontal Stretching
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Example
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Sequences of Transformations
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A function involving more than one transformation can be graphed by performing transformations in the following order: Horizontal shifting Stretching or shrinking Reflecting Vertical shifting
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Summary of Transformations
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A Sequence of Transformations
Starting graph. Move the graph to the left 3 units Stretch the graph vertically by 2. Shift down 1 unit.
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Example
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Example
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Example
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(a) (b) (c) (d)
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g(x) Write the equation of the given graph g(x). The original function was f(x) =x2 (a) (b) (c) (d)
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g(x) Write the equation of the given graph g(x). The original function was f(x) =|x| (a) (b) (c) (d)
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