Hey Ascendant78.

You usually define these kinds of things as having an asymptote or being "asymptotic".

You have two kinds of asymptotes: vertical and horizontal. Vertical ones are found in the graphs like yours where you have a vertical asymptote at x = 0 for a negative one for x approaching zero from the left and a positive one for x approaching zero on the right.

The function should always be strictly decreasing everywhere but the asymptote means that it will have a break in it and this means that it will be strictly decreasing, but only with respect to the sides of where the asymptote is.