What is the domain and range of #y = 3/x#?

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Answer 1 · 2017-07-12T13:49:02

See below.

Domain: you shall not divide by zero: #RR - {0}#

Image: by the hyperbola graph, #RR - {0}#

Answer 2 · 2017-07-12T14:12:16

Domain: #(-oo, 0)uu(0, +oo)#
Range: #(-oo, +oo)#

#y = 3/x#

#y# is defined #forall x in RR: x!=0#

Hence the domain of #y# is #(-oo, 0)uu(0, +oo)#

Now consider:

#lim_"x->0-"y =-oo#

and

#lim_"x->0+"y =+oo#

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

This can be seen from the graph of #y# below.

graph{3/x [-10, 10, -5, 5]}