Problem $1$ Based on the graph below, determine the following values. If a value do write 'DNE.$\text{'}$

$($a$)f(0)=1$

$($f$)\underset{x1}{lim}f(x)=1$

$($b$)\underset{x{0}^{+}}{lim}f(x)=1$

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

$($c$)f(1)=$DNE

$($h$)f(3)=0$

$($d$)\underset{x{1}^{+}}{lim}f(x)=1$

$($i$)\underset{x3}{lim}f(x)=3$

$($e$)\underset{x{1}^{-}}{lim}f(x)=2$

$($j$)\underset{x4}{lim}f(x)=1$