Vertical stretch

Definition

A vertical stretch is a transformation that scales a function's graph away from the x-axis by multiplying all y-values by a factor greater than 1. It does not affect the x-values of the function.

5 Must Know Facts For Your Next Test

1. A vertical stretch is represented as $y = af(x)$, where $a > 1$.
2. If $a < 1$, the transformation is called a vertical compression, not a stretch.
3. The greater the value of $a$, the more pronounced the stretching effect on the graph.
4. A vertical stretch affects only the y-coordinates of points on the graph; x-coordinates remain unchanged.
5. In combination with other transformations like translations or reflections, a vertical stretch must be applied first to maintain accuracy.

Review Questions

• What happens to the graph of $f(x)$ when it undergoes a vertical stretch with a factor of 3?
• How does a vertical stretch differ from a horizontal stretch?
• If you have $y = f(x)$ and apply a vertical stretch by a factor of 2, what will be the new equation?

Related terms

Vertical Compression:

A transformation that scales down all y-values of a function's graph by multiplying them by a factor between 0 and 1.

Horizontal Stretch:

$f(bx)$ where $0 < b < 1$ stretches the graph horizontally by dividing x-coordinates by $b$.

Transformation: Operations that alter the form of a function's graph, including translations, reflections, stretches, and compressions.