mac1105_lecture14_1

# mac1105_lecture14_1 - L14 Graphing Techniques...

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131 L14 Graphing Techniques: Transformations; Mathematical Models Transformations Vertical and Horizontal Translations: ( 0) c > To graph: shift () fx c units: fx c + + Example: Graph the function 31 yx =− .

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132 Vertical Compressions and Stretches: Example: Above is the graph of 1 3 yx = . In the same plane, graph 1 3 2 = and 1 3 1 2 = . The graph of ( ) ya f x = ( 0 a ) is obtained from the graph of ( ) yf x = by multiplying by a the y - coordinate of each point that is on the graph of f . Compared to the graph of ( ) x = , the graph of () f x = is: stretched vertically if 1 a > ; compressed vertically if 01 a << .
133 Horizontal Compressions and Stretches: 3 () fx x = 3 (2 ) fx x = 3 11 22 x ⎛⎞ = ⎜⎟ ⎝⎠ The graph of ( ) yf a x = ( 0 a ) is obtained from the graph of ( ) x = by multiplying by 1 a the x - coordinate of each point which is on the graph of f . Compared to the graph of ( ) x = , the graph of a x = is: stretched horizontally if 01 a < < ; compressed horizontally if 1 a > .

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134 Reflections across the x -Axis and y -Axis: In order to obtain the graph of ( ) yf x = − , reflect the graph of ( ) x =
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mac1105_lecture14_1 - L14 Graphing Techniques...

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