Question

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

Answer 1

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

Explanation:

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}`