Horizontal compression definition how to#

Which is graphed by the dashed parabola below. If it is translated vertically by +4, so that its vertex moves from (0,0) to (0,4), the equation becomes: Vertical DilationĬonsider the solid parabola below, which represents the function: All points that were on one side of the axis of dilation are reflected to the other side of the axis by a negative dilation factor. Note that a negative dilation factor causes both a dilation and a reflection about the axis to occur. Visualizing functions as translations and dilations of a simpler “parent function” can make complex-looking equations much easier to interpret. It was then shifted one unit to the right, just as the vertex was, and that point (3 ,17) satisfies the equation of the dashed parabola, g(x). The green point on the solid parabola (2, 4) also had its y-coordinate (4) multiplied by three and had five added to it: So, the “parent” vertex that was at the origin is located at (1, 5) in the transformed function. It was then shifted one unit to the right, causing its x-coordinate to change from 0 to 1. The blue point at the origin, which is the vertex of the solid parabola, had its y-coordinate (0) multiplied by three then had five added to it: Translationį(x) has been dilated vertically by a factor of 3, then translated vertically by +5 and horizontally by +1 to produce g(x). (graphed as the solid curve below) which has been both dilated and translated: (graphed as the dashed curve below), is easier to analyze if you perceive it as related to a simpler “parent” function: However, in general the function definition which is simplest (in algebraic terms) will be considered the “parent” function, with the more complex-looking definition being described as a dilation of the simpler function.

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.

Horizontal compression definition how to#

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