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**Consider dilating the graph of y = x2**

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

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**Consider dilating the graph of y = x2**

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

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**Consider dilating the graph of y = x2**

15 by a factor of 0.5 from the x-axis. 10 The point (x, y) maps onto the point (x, 0.5y). y = 0.5x2 5 (2,4) (2, 2) (2,2) e.g. (2, 4) x -3 -2 -1 1 2 3

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**A dilation of factor a from the x-axis transforms the graph of y = f(x) to that of y = af(x).**

(x, y) (x, ay) A dilation factor greater than 1 ‘stretches’ the graph ‘away from’ the x-axis. x A dilation factor less than 1 ‘shrinks’ the graph ‘towards’ the x-axis. x

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**Consider dilating the graph of y = x2**

15 by a factor of 2 from the y-axis. 10 The point (x, y) maps onto the point (2x, y). 5 y = 0.25x2 (2, 1) e.g. (1, 1) (1,1) (2,1) x -3 -2 -1 1 2 3

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**Consider dilating the graph of y = x2**

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

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**A dilation of factor a from the y-axis transforms the graph of y = f (x) to that of y = f ( ).**

(x, y) (ax, y) A dilation factor greater than 1 ‘stretches’ the graph ‘away from’ the y-axis. y A dilation factor less than 1 ‘shrinks’ the graph ‘towards’ the y-axis. y

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EXAMPLE 1 Compare graph of y = with graph of y = a x 1 x 1 3x3x b. The graph of y = is a vertical shrink of the graph of. x y = 1 = y 1 x a. The graph.

EXAMPLE 1 Compare graph of y = with graph of y = a x 1 x 1 3x3x b. The graph of y = is a vertical shrink of the graph of. x y = 1 = y 1 x a. The graph.

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