How do you find the domain and range of #y=-3/(4x+4) #?

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Answer 1 · 2017-06-08T02:07:13

Domain: #(-oo,-1)uu(-1,+oo)#
Range: #(-oo,+oo)#

#y = -3/(4x+4)#

#y# is defined for all real x except where #4x+4 =0#
i.e where #x=-1#

#:. y# is defined #forall x in RR: x!= -1#

Hence the domain of #y# is #(-oo,-1)uu(-1,+oo)#

#Lim_"x->-1 (-)" y = +oo#

and

#Lim_"x->-1 (+)" y = -oo#

Hence the range of #y# is #(-oo,+oo)#

This can be seen by the graph of #y# below.
graph{-3/(4x+4) [-10, 10, -5, 5]}