Stretch

Definition

A stretch is a transformation that scales a graph horizontally or vertically. It changes the shape of the graph without altering its basic structure.

5 Must Know Facts For Your Next Test

1. A vertical stretch multiplies all $y$-values of a function by a constant factor greater than 1.
2. A horizontal stretch multiplies all $x$-values of a function by a constant factor between 0 and 1.
3. The equation $f(cx)$ represents a horizontal stretch if $0 < c < 1$ and compression if $c > 1$.
4. The equation $cf(x)$ represents a vertical stretch if $c > 1$ and compression if $0 < c < 1$.
5. Stretches do not affect the asymptotes of exponential functions; they only change the rate at which the function approaches these asymptotes.

Review Questions

• What effect does multiplying an exponential function by a constant greater than 1 have on its graph?
• How would you represent a horizontal stretch in the equation of an exponential function?
• Do vertical stretches affect the horizontal asymptote of an exponential function?

Related terms

Exponential Function:

A mathematical function in the form $f(x) = ab^x$, where $a \neq 0$, $b > 0$, and $b \neq 1$. It shows rapid growth or decay.

Horizontal Compression:

A transformation that scales down the graph horizontally, represented by multiplying all $x$-values by a constant factor greater than one.

Vertical Stretch:

A transformation that scales up the graph vertically, represented by multiplying all $y$-values by a constant factor greater than one.