Function transformations. 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