Question

How do you find the domain of `1/(x+2)`?

Answer 1

You look for the values of `x` that are outside the domain.

Explanation:

If `x=-2` then `x+2=0` so the denominator of the fraction will become indefinite.
Other values of `x` are acceptable, so:

Domain `x!=-2`
Or in 'the language':
`lim_(x->-2^-) y=-oo` and `lim_(x->-2^+) y=+oo`

graph{1/(x+2) [-10, 10, -5, 5]}
As for range : as `x` gets larger, the function will approach to `0`.

`lim_(x->-oo) y=lim_(x->+oo) y=0`

So range: `y!=0`