1. `y=1/(x+4)`, find Asymptotes of a function

Solution:
Asymptotes :
Now, find domain of `y=1/(x+4)`

`y=1/(x+4)`

`x+4=0`

`=>x+4=0`

`=>x=0-4`

`=>x=-4`

Domain : `x!=-4`

Vertical asymptote : `x=-4`

The highest power in the numerator is 0
The highest power in the denominator is 1
Since highest power denominator is greater than highest power on numerator, then the horizontal asymptote will be x-axis.
Horizontal asymptote : y = 0 (x-axis)
Slant(Oblique) asymptote : none