Answer
$a.\qquad $see image below
$b.\quad (-\infty,\infty)$
$ c.\quad$ Decreases on $( 0,\infty)$
Increases on $ ( -\infty,0)$
Work Step by Step
$a.$
(graphed with online graphic calculator at desmos.com)
$b.$
$f$ is defined for all reals, $(-\infty,\infty)$
$c.$
f has a local maximum at $x=0$
Decreases on $( 0,\infty)$
Increases on $ ( -\infty,0)$