Answer
See the image below.
Work Step by Step
Normally, to sketch a graph we need to assign several main points. At first we need to assign $0$ for any possible case, then couple of positive and negative numbers (preferable numbers like $1$ & $-1$, $2$ & $-2$, $3$ & $-3$ etc.).
Using the method, we can graph it by hand by simply connecting points. But for a better visualization it will be represented by a graphing calculator on the image above.
(a) $f(x)=x^2$
$x=0$; $y=0$
$x=1$; $y=1$
$x=2$; $y=4$
$x=-1$; $y=1$
$x=-2$; $y=4$
Connecting these points will give us the $Black$ graph $(a)$ shown in the image above.
(b) $g(x) = x^3$
$x=0$; $y=0$
$x=1$; $y=1$
$x=2$; $y=8$
$x=-1$; $y=-1$
$x=-2$; $y=-8$
Connecting these points will give us the $Green$ graph $(b)$ shown in the image above.
(c) $h(x)=|x|$
$x=0$; $y=0$
$x=1$; $y=1$
$x=2$; $y=2$
$x=3$; $y=3$
$x=-1$; $y=1$
$x=-2$; $y=2$
$x=-3$; $y=3$
Connecting these points will give us the $Red$ $(c)$graph in the image above.
(d) $k(x)=\sqrt{x}$
$x=0$; $y=0$
$x=1$; $y=1$
$x=4$; $y=2$
$x=9$; $y=3$
