Mainly there are three types of asymptotes:
1) Horizontal asymptotes,
2) Vertical asymptotes and
3) Oblique asymptotes.
For a graph which is represented by Function x = f(y), horizontal asymptotes are horizontal lines. These asymptotes are obtained when function approaches zero as 'y' tends to +∞ or −∞.
Vertical asymptotes are vertical lines near the asymptotes, the function expands without any bounds.
Let’s try to understand oblique asymptote and Graphing Oblique Asymptotes.
Oblique asymptote is a linear asymptote. When this linear asymptote is not parallel to the x or y- axis then it is called as oblique asymptote. Oblique asymptote is also called as slant asymptote.
Let’s consider the following function f(y) = y + 1/y’ and plot its graph. Here in above graph line x = y and x- axis are both asymptotes.
A function f(y) is asymptotic to Straight Line x = my + c ( if m ≠ 0) if
Lim (y→ +∞) [f (y) - (my + c)] = 0,
Lim (y→ - ∞) [f (y) - (my + c)] = 0,
Among these two equations, equation x = my + c is an oblique asymptote of ƒ(y) when 'y' tends to +∞, and in second equation, line x = my + c is an oblique asymptote of ƒ (y) when 'y' tends to −∞.
Oblique asymptotes can also be defined for rational Functions.