Question

How do you find the domain and range of `g(x)= (3x)/(2x-5)`?

Answer 1

For the domain there is only the restriction that `x!=2 1/2`
This would make the numerator `=0`

Explanation:

In the "language" we say:

`lim_(x->2 1/2) g(x)= oo` and `x=2 1/2` is the vertical asymptote

As `x` gets larger the function will tend to look more and more like

`(3x)/(2x)=1 1/2` without quite getting there, or:

`lim_(x->oo) g(x)=1 1/2` or `g(x)=1 1/2` is the horizontal asymptote

So the range has as only restriction `g(x)!=1 1/2`

graph{3x/(2x-5) [-10.98, 21.04, -5.92, 10.1]}