Dilations

# Dilations - -1 1 2 3 5 10 15 The point x y maps onto the...

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Dilations x y -3 -2 -1 0 1 2 3 5 10 15 y = x 2 y = 2 x 2 The point ( x , y ) maps onto the point ( x , 2 y ). Consider dilating the graph of y = x 2 by a factor of 2 from the x -axis. e.g. (2, 4) (2, 8) (2,8) (2,4)

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Dilations x y -3 -2 -1 0 1 2 3 5 10 15 The point ( x , y ) maps onto the point ( x , 3 y ). Consider dilating the graph of y = x 2 by a factor of 3 from the x -axis. e.g. (2, 4) (2, 12) y = 3 x 2 (2,12) y = x 2 (2,4)
Dilations x y -3 -2 -1 0 1 2 3 5 10 15 The point ( x , y ) maps onto the point ( x , 0.5 y ). Consider dilating the graph of y = x 2 by a factor of 0.5 from the x -axis. e.g. (2, 4) (2, 2) y = 0.5 x y = x 2 (2,4) (2,2)

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Dilations A dilation factor greater than 1 ‘stretches’ the graph ‘away from’ the x -axis. A dilation factor less than 1 ‘shrinks’ the graph ‘towards’ the x -axis. ( x , y ) ( x , ay ) A dilation of factor a from the x -axis transforms the graph of y = f ( x ) to that of y = af ( x ). x x
Dilations x y -3 -2

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Unformatted text preview: -1 1 2 3 5 10 15 The point ( x , y ) maps onto the point (2 x , y ). Consider dilating the graph of y = x 2 by a factor of 2 from the y-axis. e.g. (1, 1) (2, 1) → y = 0.25 x y = x 2 (1,1) (2,1) Dilations x y-3-2-1 1 2 3 5 10 15 The point ( x , y ) maps onto the point (0.5 x , y ). Consider dilating the graph of y = x 2 by a factor of 0.5 from the y-axis e.g. (2, 4) (1, 4) → y = 4 x 2 (1,4) y = x 2 (2,4) Dilations A dilation factor greater than 1 ‘stretches’ the graph ‘away from’ the y-axis. A dilation factor less than 1 ‘shrinks’ the graph ‘towards’ the y-axis. ( x , y ) → ( ax , y ) A dilation of factor a from the y-axis transforms the graph of y = f ( x ) to that of y = f ( ). x a y y...
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## This note was uploaded on 04/12/2011 for the course MATH 2180 taught by Professor Staff during the Spring '11 term at North Texas.

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Dilations - -1 1 2 3 5 10 15 The point x y maps onto the...

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