g$($x$)=($x $3)/[($x$^2+1)]($a$)$ Identify the domain and determine whether this function have any vertical or horizontal asymptotes? If so$,$ where? $($b$)$ Identify the interval$($s$)$ in which f is increasing$/$decreasing and classify the critical point$($s$)$ of f as local max$/$min or neither. $($c$)$ Identify the intervals of concave up$/$down and find the point$($s$)$ of inflection.