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Dilations x y -3-20123 5 10 15 y = x 2 y = 2x 2 The point (x, y) maps onto the point (x, 2y). Consider dilating the graph of y = x 2 by a factor of 2 from.

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Presentation on theme: "Dilations x y -3-20123 5 10 15 y = x 2 y = 2x 2 The point (x, y) maps onto the point (x, 2y). Consider dilating the graph of y = x 2 by a factor of 2 from."— Presentation transcript:

1 Dilations x y -3-20123 5 10 15 y = x 2 y = 2x 2 The point (x, y) maps onto the point (x, 2y). Consider dilating the graph of y = x 2 by a factor of 2 from the x-axis. e.g. (2, 4) (2, 8)  (2,4)

2 Dilations x y -3-20123 5 10 15 The point (x, y) maps onto the point (x, 3y). Consider dilating the graph of y = x 2 by a factor of 3 from the x-axis. e.g. (2, 4) (2, 12)  y = 3x 2 (2,12) y = x 2 (2,4)

3 Dilations x y -3-20123 5 10 15 The point (x, y) maps onto the point (x, 0.5y). 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 = 0.5x 2 y = x 2 (2,4) (2,2)

4 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

5 Dilations x y -3-20123 5 10 15 The point (x, y) maps onto the point (2x, 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 = 0.25x 2 y = x 2 (1,1) (2,1)

6 Dilations x y -3-20123 5 10 15 The point (x, y) maps onto the point (0.5x, 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 = 4x 2 (1,4) y = x 2 (2,4)

7 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 ( ). y y


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