##<b>Function transformations.</b> Suppose $f$ is a function, and $c>0$. The graph of #$y=f(x)+c$ is the graph of $f$ shifted $c$ units up #$y=f(x)-c$ is the graph of $f$ shifted $c$ units down #$y=f(x+c)$ is the graph of $f$ shifted $c$ units left #$y=f(x-c)$ is the graph of $f$ shifted $c$ units right ##Now suppose $c>1$. The graph of #$y=cf(x)$ is the graph of $f$ stretched vertically by a factor $c$ #$y=(\frac{1}{c})f(x)$ is the graph of $f$ compressed vertically by a factor $c$ #$y=f(cx)$ is the graph of $f$ compressed horizontally by a factor $c$ #$y=f(x/c)$ is the graph of $f$ stretched horizontally by a factor $c$ #$y=-f(x)$ is the graph of $f$ reflected about the $x$-axis #$y=f(-x)$ is the graph of $f$ reflected about the $y$-axis