Compression

Definition

Compression in algebra and trigonometry refers to the transformation that scales a graph towards an axis, making it narrower. This is achieved by multiplying the function by a constant factor.

5 Must Know Facts For Your Next Test

1. Vertical compression occurs when the y-values of a function are multiplied by a factor between 0 and 1.
2. Horizontal compression happens when the x-values of a function are multiplied by a factor greater than 1.
3. A compressed exponential graph will appear to grow or decay more slowly compared to its original form.
4. Logarithmic functions can also undergo compression, affecting their rate of increase or decrease.
5. The transformation rule for vertical compression in the function $f(x)$ is given by $g(x) = cf(x)$ where $0 < c < 1$.

Review Questions

• What effect does multiplying the y-values of an exponential function by 0.5 have on its graph?
• How would you describe horizontal compression for a logarithmic function?
• What is the general form for vertical compression of a linear function?

Related terms

Vertical Stretch: Transformation that scales a graph away from the x-axis, making it taller.

Horizontal Stretch: Transformation that scales a graph away from the y-axis, making it wider.

$f(cx)$: $f(cx)$ represents horizontal transformations, including both stretches and compressions depending on whether $c$ is less than or greater than 1.