Vertical compression

Definition

A vertical compression is a transformation that scales a function's graph towards the x-axis. This is achieved by multiplying the function by a constant factor between 0 and 1.

5 Must Know Facts For Your Next Test

1. A vertical compression of $f(x)$ by a factor of $c$ (where $0 < c < 1$) is represented by the transformed function $g(x) = c \cdot f(x)$.
2. Vertical compressions reduce the y-values of the function, making the graph appear 'flatter'.
3. The x-intercepts of the function remain unchanged during a vertical compression.
4. Vertical compression affects all points on the graph equally, changing their distance from the x-axis but not their horizontal positions.
5. If $c > 1$, it results in a vertical stretch instead of a vertical compression.

Review Questions

• What happens to the y-values of a function when it undergoes a vertical compression?
• How do you represent a vertical compression mathematically if given $f(x)$ and a compression factor $c$?
• Does vertical compression change the x-intercepts of the original function?

Related terms

Vertical Stretch:

A transformation that scales a function’s graph away from the x-axis, achieved by multiplying the function by a constant factor greater than 1.

Horizontal Compression:

A transformation that scales a function’s graph towards the y-axis, achieved by multiplying each x-coordinate by a constant factor greater than 1.

Transformation: \text{An operation that modifies} \, \text{a graph's position or shape, such as translations, reflections, stretches, and compressions.}