Algebra 2. Transformation of Fucntions.

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Vertical compression involves "squishing" points toward the x-axis, with invariant points located on the x-axis, while horizontal compression compresses points toward the y-axis, with invariant points on the y-axis. An example is the function f(x) = 4x^2, which represents a vertical stretch of the graph of y = x^2 by a factor of 2, but can also be viewed as a horizontal compression by a factor of 1/2. Understanding these transformations is crucial for analyzing function behavior. The relationship between vertical and horizontal transformations can sometimes lead to equivalent results depending on the axis considered. Mastery of these concepts is essential for success in Algebra 2.
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Whats the difference between "Vertical Compression" and "Horizontal Compression"? Can you give me couple example? Thank you.
 
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A vertical compression is "squishing" all points towards the x-axis, it is also important to rember that the invariant points in such a transformation are ON the x-axis. A horizontal compression is "squishing" all points towards the y-axis. It is important to remember that all invariant points are on the y-axis. However, there are some cases where a transformation is equivalent to another transformation relative to a different axis.
Consider the function f(x) = 4x^2 This is a transformation of the graph of y = x^2 vertically stretched by a factor of 2. However, this is also equivalent to a horizontal compression by a factor of 1/2.
 
Thank you very much.
 

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