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Section 2.5 Transformation of Functions. Graphs of Common Functions. Reciprocal Function. Vertical Shifts. Vertical Shifts. Example. Use the graph of f(x)=|x| to obtain g(x)=|x|-2. Horizontal Shifts. Horizontal Shifts. Example. Use the graph of f(x)=x 2 to obtain g(x)=(x+1) 2.

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## Section 2.5 Transformation of Functions

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**Example**Use the graph of f(x)=|x| to obtain g(x)=|x|-2**Example**Use the graph of f(x)=x2 to obtain g(x)=(x+1)2**Example**Use the graph of f(x)=x2 to obtain g(x)=(x+1)2+2**Example**Use the graph of f(x)=x3 to obtain the graph of g(x)= (-x)3.**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.**Example**Use the graph of f(x)=|x| to graph g(x)= 2|x|**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**A Sequence of Transformations**Starting graph. Move the graph to the left 3 units Stretch the graph vertically by 2. Shift down 1 unit.**(a)**(b) (c) (d)**g(x)**Write the equation of the given graph g(x). The original function was f(x) =x2 (a) (b) (c) (d)**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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