Stretch

Definition

A stretch is a transformation that alters the shape of a graph by scaling it vertically or horizontally. It affects the distance between points on the graph without changing their relative positions.

5 Must Know Facts For Your Next Test

1. Vertical stretches are represented by multiplying the function by a constant factor greater than 1, $f(x) \rightarrow af(x)$ where $a>1$.
2. Horizontal stretches involve scaling the input variable by a factor, represented as $f(x) \rightarrow f(bx)$ where $0 < b < 1$.
3. A vertical stretch makes the graph taller, while a horizontal stretch makes it wider.
4. If $a$ is between 0 and 1 in a vertical stretch, it compresses the graph instead of stretching it.
5. Stretches do not affect the x-intercepts or y-intercepts of exponential functions.

Review Questions

• What impact does multiplying an exponential function by a constant greater than 1 have on its graph?
• How do you represent a horizontal stretch in an exponential function?
• Does a vertical stretch change the x-intercepts or y-intercepts of an exponential function?

Related terms

Compression: A transformation that reduces the size of a graph either vertically or horizontally.

Translation: A transformation that shifts a graph horizontally or vertically without changing its shape.

Reflection: A transformation that flips a graph over a specified axis, altering its orientation.