mac1105_lecture14_2 - L14 Graphing Techniques...

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131 L14 Graphing Techniques: Transformations; Mathematical Models Transformations Vertical and Horizontal Translations: ( 0) c > To graph: shift ( ) f x c units: ( ) f x c + ( ) f x c ( ) f x c + ( ) f x c Example: Graph the function 3 1 y x = . 132 Vertical Compressions and Stretches: Example: Above is the graph of 1 3 y x = . In the same plane, graph 1 3 2 y x = and 1 3 1 2 y x = . The graph of ( ) y a f x = ( 0 a ) is obtained from the graph of ( ) y f x = by multiplying by a the y - coordinate of each point that is on the graph of f . Compared to the graph of ( ) y f x = , the graph of ( ) y a f x = is: stretched vertically if 1 a > ; compressed vertically if 0 1 a < < .
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