![]() Below you can see a variety of vertical stretches, compressions, and/or reflections on the function f\left(x\right)=x. Another transformation that can be applied to a function is a reflection over the x- or y-axis. A vertical reflection reflects a graph vertically across the x. This means the larger the absolute value of m, the steeper the slope. Another transformation that can be applied to a function is a reflection over the x or y-axis. The easiest way to do a reflection about another horizontal or vertical line is to: Draw the line Consider the line and original object as one figure. Notice in the figure below that multiplying the equation of f\left(x\right)=x by m vertically stretches the graph of f by a factor of m units if m>1 and vertically compresses the graph of f by a factor of m units if 0reflect a parent function horizontally, replace x with -x in the function. When m is negative, there is also a vertical reflection of the graph. To reflect a parent function vertically, multiply the entire function by -1. Horizontal reflection can be represented by the following algorithm: x' -x where x is the x-coordinate and x' is the result of the reflection. To produce a vertical reflection, y-coordinates are multiplied by -1. To produce a horizontal reflection, x-coordinates are multiplied by -1. In the equation f\left(x\right)=mx, the m is acting as the vertical stretch or compression of the identity function. In short, reflection is just negative scaling. Before moving on, make sure to review math transformations and coordinate geometry. Often, this line is the x-axis, y-axis, or the line y x. A function may also be transformed using a reflection, stretch, or compression. Reflection in Geometry Reflection in Geometry Explanation, and Examples A reflection in geometry is the transformation of an object by creating a mirror image of it on the other side of a given line. ![]() A function may be transformed by a shift up, down, left, or right. Graphing a Linear Function Using TransformationsĪnother option for graphing linear functions is to use transformations of the identity function f\left(x\right)=x. ![]()
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