A graph can be horizontally or vertically scaled by multiplying each $x$ or $y$ coordinate of the graph by a constant factor. This can be represented in function form as $a\cdot f\left(x\right)$ for a vertical scaling, or $f\left(b\cdot x\right)$ for a horizontal scaling.
A graph is vertically compressed if the $y$ values for a given $x$ value become smaller. If the $y$ values become larger, the graph is vertically stretched. Vertical stretches occur when $\lefta\right\>1$, while compressions occur when $\lefta\right<1$. If $a\=1$, the graph is not affected, while if $a<0$, the graph is reflected across the $x$axis, as well as stretched or compressed.
Similarly, a graph is horizontally compressed if the $x$ values decrease for a given $y$ value. If they increase, the graph is horizontally stretched. Horizontal scaling, like translations, are the opposite of what is expected. Stretches occur when $\leftb\right<1$, while compressions occur when $\leftb\right\>1$. If $b\=1$, the graph is not affected, while if $b<0$, the graph is reflected across the $y$axis, as well as stretched or compressed.
