stretchingcompressing

Stretching and compressing refer to transformations applied to geometric shapes, functions, or data sets to alter their size or spacing along one or more axes. These transformations are fundamental concepts in mathematics, particularly in algebra, geometry, and calculus, as well as in fields like physics, engineering, and computer graphics.

In the context of functions, stretching and compressing typically refer to vertical or horizontal transformations. A vertical stretch or compression affects the *y*-values of a function, altering its steepness or flatness. For example, multiplying a function *f(x)* by a constant *a* (where *a* > 1) results in a vertical stretch by a factor of *a*, making the graph taller. Conversely, if *0 < a < 1*, the graph undergoes a vertical compression, making it shorter. Similarly, horizontal transformations occur when the input *x* is scaled by a factor *b*. If *b* > 1, the graph stretches horizontally, while *0 < b < 1* compresses it.

In geometry, stretching and compressing can refer to scaling transformations, where an object is uniformly or non-uniformly enlarged or reduced in size relative to a fixed point called the center of scaling. Non-uniform scaling involves different scaling factors along different axes, distorting the shape while preserving its angles in some cases. For instance, stretching a square along the *x*-axis while keeping the *y*-axis unchanged transforms it into a rectangle.

These transformations are also applied in data visualization, where axes may be stretched or compressed to better represent data trends or accommodate varying scales. In physics, stretching and compressing describe how materials deform under stress, influencing properties like elasticity and rigidity. Understanding these concepts is essential for analyzing motion, forces, and structural integrity in mechanical systems.