Using tacogym's analogy, heres what he's saying -
y= x + 1/x
If we graph y = x and y = 1/x, and add them on, as x -> infinity, the graph approaches y = x
You can tell it approaches above the line y= x because it's an addition of 1/x, but if it was a negative, it would approach from below the assymptote.
In 2unit/3unit - general rule is just dividing all terms by the HIGHEST degree in the denominator.
ie. 3x+5/x^2+x highest degree is x^2, division gives.
(3/x+5/x)/(1+1/x) - as x -> infinity
3/x -> 0
5/x -> 0
1/x -> 0
so you have 0/1 = 0
thus the line y = 0 is an asymptote.