mac1147_lecture13_1_c

# mac1147_lecture13_1_c - L13 Graphing Techniques...

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132 L13 Graphing Techniques: Transformations; Quadratic Functions and Models Vertical and Horizontal Translations : ( 0) c > To graph: shift () fx c units: fx c + + Example : Graph the function 31 yx =− .

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133 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 << .
134 Horizontal Compressions and Stretches : 3 () fx x = 3 (2 ) 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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135 Reflections about the x -Axis and the y -Axis : The graph of ( ) yf x =− is a reflection of the graph of ( ) x = across the x-axis .
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## This note was uploaded on 11/07/2011 for the course MAC 1147 taught by Professor German during the Summer '08 term at University of Florida.

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mac1147_lecture13_1_c - L13 Graphing Techniques...

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