An Asymptote is actually a line whose distance with curve approaches zero as they approach infinity and this line (asymptote) never touches the curve. Line will always be close to curve but it will not intersect the curve.
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.