How do you find the domain and range of #g(x)=2/x#?

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Answer 1 · 2018-06-10T13:14:23

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

#g(x) = 2/x#

#g(x)# is defined #forall x !=0#

Hence, the domain of #g(x)# is : #(-oo,0)uu(0,+oo)#

Now consider the limit of #g(x)# as #x-> 0# from below and from above.

#lim_(x->0^-) 2/x -> -oo#

#lim_(x->0^+) 2/x -> +oo#

Thus #g(x)# has a vertical asymptote at #x=0#.

The range of #g(x)# is therefore #(-oo,+oo)#

We can visualise these results from the graph of #g(x)# below.

graph{2/x [-10, 10, -5, 5]}