The function

f$($x$)$

is graphed below. It has domain

$(\backslash$infty $,\backslash$infty $).$

The x y$-$coordinate plane is given. A curve with $2$ parts is graphed.

The first part is linear, enters the window in the second quadrant, goes down and right, passes through the point $(6,4),$ crosses the x$-$axis at x $=4\mathrm{.}5,$ passes through the approximate point $(4,1\mathrm{.}3),$ and ends at the point $(3,4).$

The second part is a curve, begins at the point $(3,4),$ goes up and right becoming less steep, changes direction at the origin, goes down and right becoming more steep, passes through the point $(3,4),$ and exits the window in the fourth quadrant.

Find the absolute maximum and absolute minimum y$-$values of

f$($x$)$

on the given intervals, if they exist. $($If an answer does not exist, enter DNE.$)$

$($a$)$

$(\backslash$infty $,\backslash$infty $)$

absolute maximum

absolute minimum

$($b$)$

$[4,3]$

absolute maximum

absolute minimum

$($c$)$

$[3,0)$

absolute maximum

absolute minimum