#f(x)=(x-2)^2+9#
There are no restrictions on #x# so domain of #f(x)# is:
#{x in RR }#
Minimum value of #f(x)#
#y= ((2)-2)^2+9=(0)^2+9=9#
as #x-> +-oo# , #color(white)(88)(x-2)^2+9-> oo#
(#( x-2)^2#is always positive or zero )
So range is:
#{y in RR | 9 <= y < oo}#
Graph: