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

1 Answer
Jun 10, 2018

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

Explanation:

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]}