Question

How do you find the domain and range of `y=1/(x-4)`?

Answer 1

The only restriction on the domain is `x!=4`
As this would make the numerator `=0`

Explanation:

As `x` nears `4` from above, `y` will be larger and larger, or in "the language":
`lim_(x->4+) y = oo`
Something like that goes if `x` nears `4` from below:
`lim_(x->4-) y = -oo`
`x=4` is called the vertical asymptote.

`y` can never reach the value of `0` ( horizontal asymptote), so th range is `y!=0`, or:
`lim_(x->oo) y=0`

graph{1/(x-4) [-5.04, 14.96, -4.24, 5.76]}