Equations - Streching

Stretching and Compressing

Definition and Vertical Transformations

Stretching and compressing refer to vertical transformations of a graph that change its steepness or flatness. These are controlled by multiplying the function by a constant: \[ g(x) = C f(x) \] where the value of \( C \) determines whether the graph stretches or compresses vertically.

Graph showing vertical stretching and compressing

How It Works

  • \( 0 < C < 1 \): Vertical compression. The graph is squashed toward the x-axis.
    Example: \( g(x) = \frac{1}{2}f(x) \)
  • \( C > 1 \): Vertical stretching. The graph is pulled away from the x-axis.
    Example: \( h(x) = 2f(x) \)
  • Only the y-values change; x-values remain the same.

Applications

  • Used to model scaling in real-world graphs, like sound waves or population growth.
  • Helpful in animating and transforming shapes in computer graphics.
  • Important in data visualization for adjusting trends and slopes.
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