How do you find the domain and range of #y=5/(x-1)#?

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Answer 1 · 2016-12-24T14:19:10

The domain is #=RR-{1}#
The range is #=RR-{0}#

As you cannot divide by #0#, #=>#, #x!=1#

Therefore,

The domain of #x# is #D_x=RR-{1}#

The limit of #y# as #x->oo# is

#lim_(x->-oo)y=lim_(x->-oo)5/x=0^(-)#

#lim_(x->+oo)y=lim_(x->+oo)5/x=0^(+)#

There is a horizontal asymptote at #y=0#

Therefore,

The range is #R_y =RR-{0}#