Compression

Definition

Compression refers to a transformation that reduces the distance between points in a graph. It often results in the graph appearing 'squeezed' either horizontally or vertically.

5 Must Know Facts For Your Next Test

1. Horizontal compression occurs when the input variable is multiplied by a factor greater than 1.
2. Vertical compression happens when the output of a function is multiplied by a factor between 0 and 1.
3. The compressed graph retains the original shape but with altered dimensions.
4. For exponential functions, horizontal compression can make growth appear faster.
5. For logarithmic functions, vertical compression can make growth appear slower.

Review Questions

• What effect does multiplying the input variable of a function by a factor greater than 1 have on its graph?
• How does vertical compression affect the appearance of an exponential function's graph?
• What remains unchanged in a function's graph after it undergoes compression?

Related terms

Horizontal Stretch:

A transformation that increases the distance between points horizontally, making the graph wider.

Vertical Stretch:

A transformation that increases the distance between points vertically, making the graph taller.

$y = c \cdot f(x)$: $y = c \cdot f(x)$ represents vertical scaling of a function, where $c$ is a constant.