Vertical stretch

Definition

A vertical stretch is a transformation that scales a function's graph vertically by a factor greater than 1, making it appear taller. It multiplies the output value (y-coordinate) of each point by a given factor.

5 Must Know Facts For Your Next Test

1. A vertical stretch changes the y-values of a function but leaves the x-values unchanged.
2. The factor of the vertical stretch is often represented as 'a' in $y = af(x)$, where $|a| > 1$.
3. Vertical stretches do not affect the x-intercepts of the graph.
4. If $a < -1$, it results in both a vertical stretch and reflection over the x-axis.
5. Vertical stretches are different from horizontal stretches, which affect the x-coordinates instead.

Review Questions

• What happens to the y-coordinates of a function when it undergoes a vertical stretch?
• How does a vertical stretch transformation differ from a horizontal stretch?
• If given the function $y = 2f(x)$, what type of transformation has occurred?

Related terms

Horizontal Stretch: A transformation that scales a function's graph horizontally by a factor greater than 1, affecting the x-coordinates.

Vertical Compression: A transformation that scales down or compresses the y-values of a function's graph by multiplying them by a factor between 0 and 1.

Reflection: $\text{A geometric transformation that flips a function’s graph over an axis.}$