![]() ![]() So far we have understood the types of transformations of functions and how do addition/subtraction/multiplication/division of a number and the multiplication of a minus sign would reflect a graph. For example, the point (1, 1) (on the original graph) corresponds to (1, 3) on the new graph. In the following graph, the original function y = x 3 is stretched vertically by a scale factor of 3 to give the transformed function graph y = 3x 3. Every old y-coordinate is multiplied by k to find the new y-coordinate. In this dilation, there will be changes only in the y-coordinates but there won't be any changes in the x-coordinates. It changes a function y = f(x) into the form y = f(kx), with a scale factor '1/k', parallel to the x-axis. The horizontal dilation (also known as horizontal scaling) of a function either stretches/shrinks the curve horizontally. Similarly, if it is dilated parallel to the y-axis, all the y-values are increased by the same scale factor. If a graph undergoes dilation parallel to the x-axis, all the x-values are increased by the same scale factor. Here, the original function y = x 2 (y = f(x)) is moved to 2 units up to give the transformed function y = x 2 + 2 (y = f(x) + 2).Ī dilation is a stretch or a compression.
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