Horizontal compression

Definition

Horizontal compression is a transformation that narrows the graph of a function horizontally. It occurs when all $x$-coordinates are multiplied by a factor greater than 1.

5 Must Know Facts For Your Next Test

1. A horizontal compression by a factor of $c$ is represented as $f(cx)$ where $c > 1$.
2. It reduces the distance between points on the graph along the x-axis.
3. Horizontal compression does not affect the y-coordinates of points on the graph.
4. The period of trigonometric functions is affected by horizontal compressions; for example, $\sin(2x)$ has half the period of $\sin(x)$.
5. Graphically, horizontal compression makes the function appear 'squeezed' towards the y-axis.

Review Questions

• What happens to the graph of $f(x)$ when it undergoes a horizontal compression?
• How do you express a function that has been horizontally compressed by a factor of 3?
• Does horizontal compression affect the y-values of a function's graph?

Related terms

Horizontal Stretch: A transformation that widens the graph of a function horizontally by multiplying all $x$-coordinates by a factor between 0 and 1.

Vertical Compression: $y$-coordinates are multiplied by a factor between 0 and 1, making the graph narrower vertically.

Period: The interval length over which a periodic function repeats its values. Horizontal compressions change this interval in trigonometric functions.