TextPuzzle

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