Horizontal compression

Definition

Horizontal compression transforms a function by reducing its width. It is achieved by multiplying the input variable by a factor greater than 1.

5 Must Know Facts For Your Next Test

1. The general form for horizontal compression is $f(bx)$, where $b > 1$.
2. A horizontal compression makes the graph of the function narrower.
3. If $f(x)$ is horizontally compressed by a factor of $b$, then each $x$-coordinate in the original function is divided by $b$.
4. Horizontal compression affects only the x-coordinates; y-coordinates remain unchanged.
5. The inverse operation of horizontal compression is horizontal stretching.

Review Questions

• What does it mean to horizontally compress a function?
• In the transformation $f(3x)$, what is the factor of horizontal compression?
• How does horizontal compression affect the x-coordinates of a function?

Related terms

Horizontal Stretching: Transforms a function by widening its width. Achieved by multiplying the input variable by a factor between 0 and 1.

Vertical Compression: Reduces the height of a function's graph. Achieved by multiplying the output variable by a factor between 0 and 1.

Transformation: An operation that alters the form of a function, including translations, reflections, stretches, and compressions.