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.