Horizontal stretch

Definition

A horizontal stretch is a transformation that scales a function's graph horizontally by multiplying the input values by a constant factor. If $0 < k < 1$, the graph stretches away from the y-axis.

5 Must Know Facts For Your Next Test

1. A horizontal stretch affects the x-coordinates of points on the graph.
2. The transformation is represented as $y = f(kx)$ where $0 < k < 1$.
3. If $k > 1$, it is called a horizontal compression, not a stretch.
4. A horizontal stretch makes the graph wider.
5. This transformation does not affect the y-intercepts of the function.

Review Questions

• What happens to a function's graph when it undergoes a horizontal stretch?
• How do you mathematically represent a horizontal stretch in an equation?
• What is the difference between a horizontal stretch and a horizontal compression?

Related terms

Horizontal Compression:

A transformation that scales a function's graph horizontally by multiplying the input values by a constant factor greater than 1, making it narrower.

Vertical Stretch:

A transformation that scales a function's graph vertically by multiplying the output values by a constant factor greater than 1.

Transformation: An operation that moves or changes a function in some way, including translations, reflections, stretches, and compressions.