Horizontal stretch

Definition

A horizontal stretch is a transformation that scales a function's graph horizontally by a factor. This changes the x-coordinates of every point on the graph while keeping the y-coordinates unchanged.

5 Must Know Facts For Your Next Test

1. A horizontal stretch by a factor of $k$ transforms $f(x)$ to $f\left(\frac{x}{k}\right)$.
2. If $0 < k < 1$, the graph stretches away from the y-axis.
3. If $k > 1$, the graph compresses towards the y-axis.
4. Horizontal stretches do not affect the vertical position or shape of the graph, only its width.
5. The inverse operation of a horizontal stretch is a horizontal compression.

Review Questions

• What happens to the function $f(x)$ when it undergoes a horizontal stretch by a factor of $2$?
• How does a horizontal stretch differ from a vertical stretch?
• Describe how you would transform $f(x)$ into $f\left(\frac{x}{3}\right)$ and explain what this does to the graph.

Related terms

Vertical Stretch: A transformation that scales a function's graph vertically by multiplying all y-coordinates by a factor.

Horizontal Compression: A transformation that scales down a function's graph horizontally, effectively compressing it towards the y-axis.

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