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Answer 1 · 2017-05-17T12:14:39

Domain : #x <= -3 or x >= 0 or (-oo,3] uu [0,oo)#
Range : # y >=0

#y=sqrt(x^2+3x)# , Domain: under root must be #>=0 or

#x (x+3) >= 0# critical points are #x=0 , x= -3#

when #x <= -3#; # x (x+3) >= 0# and

when #x >= 0#; # x (x+3) >= 0# and

when #-3 < x < 0 # ; # x (x+3) <= 0 #

So Domain : #x <= -3 or x >= 0 or (-oo,3] uu [0,oo)#

Range : # y >=0 or [0,oo) # graph{(x^2+3x)^0.5 [-40, 40, -20, 20]} [Ans]