dilation

dilation - Stretching and shrinking graphs parallel to the...

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Unformatted text preview: Stretching and shrinking graphs parallel to the x and y axes The graph of = y a ( ) f x for a > 0 is obtained by scaling all the y coordinates on the graph of = y ( ) f x with the factor a . To form the graph of = y a ( ) f x , the graph of = y ( ) f x is stretched parallel to the y axis if a > 1 and shrunk parallel to the y axis if < a < 1. _______________ For an example we plot some graphs of the form = y a x , where a > 1. Specifically we take = a 1, 1 1 2 , 2, 2 1 2 , 3. x | 1 4 1 9 4 4 25 4 9 ___ ___ ___ ___ ___ ___ ___ ___ ___ x | 1 2 1 3 2 2 5 2 3 3 x 2 | 3 4 3 2 9 4 3 15 4 9 2 2 x | 1 2 3 4 5 6 5 x 2 | 5 4 5 2 15 4 5 25 4 15 2 3 x | 3 2 3 9 2 6 15 2 9 This table of values may be used to help in drawing the graphs of = y x ( red ), = y 3 x 2 ( orange ), = y 2 x ( purple ), = y 5 x 2 ( green ) and = y 3 x ( maroon ). Now we plot some graphs of the form = y a x , where < a ≤ 1. Specifically we take = a 1, 3 4 , 1 2 , 1 4 ....
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dilation - Stretching and shrinking graphs parallel to the...

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