Consider the floor function $g(x)={|}_{{?}_{?}}{x}_{{?}_{?}}|.$ This function returns the greatest whole integer less than $x.$ Evaluate the following limits via simplification and graphing. If the limit does not exist, explain why. Show all work, including rough sketches of graphs.

$($a$)\underset{x{2}^{}}{lim}g(x)$

$($b$)\underset{x{2}^{-}}{lim}g(x)$

$($c$)\underset{x2}{lim}g(x)$

$($d$)\underset{xe}{lim}g(x)$