![]() the dashed line has been “dilated vertically by a factor of 0.5” to produce the solid line.īoth statements describe the graph accurately.the solid line has been “dilated vertically by a factor of 2” to produce the dashed line, or.There are two ways we can describe the relationship between the two functions graphed above. Any point that satisfies a function definition and lies on the x-axis will not move when the function is dilated vertically. The origin is a point shared by both lines, and it is useful to note that the dashed line is still “twice as far from the x-axis” at the origin, because. The coordinates of two points on the solid line are shown, as are the coordinates of the two corresponding points on the dashed line, to help you verify that the dashed line is exactly twice as far from the x-axis as the same color point on the solid line. The graph above shows a function before and after a vertical dilation. ![]() As an example of this, consider the following graph: Doing so “dilates” the graph, causing all points to move away from the axis to a multiple of their original distance from the axis. Now grasp the elastic paper with both hands, one hand on each side of the axis that is fixed to the surface, and pull both sides of the paper away from the axis. Imagine a graph that has been drawn on elastic graph paper, and fastened to a solid surface along one of the axes. If you are not familiar with “translation”, which is a simpler type of transformation, you may wish to read Function Translations: How to recognize and analyze them first.Ī function has been “dilated” (note the spelling… it is not spelled or pronounced “di alated”) when it has been stretched away from an axis or compressed toward an axis. This post explores one type of function transformation: “dilation”. For the approach I now prefer to this topic, which uses transformation equations, please follow this link: Function Transformations: Dilation
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