Vertical Asymptote

In Asymptote the distance between the curve and line approaches to zero but it never intersect and tends to infinity.
Let’s see different types of asymptote which are shown below:
Vertical asymptote,
Horizontal asymptote:
Let’s have a small introduction about both the asymptotes. First we will see the vertical asymptote. As we know that, equation of vertical line is given by:
⇒x = s;
The given equation is a vertical asymptotes of the graph which has a function y = f (s); this given function is applicable when one of the given condition is true.
The two conditions are shown below:
1. lim _{s → a-} f (s) = + ∞;
2. lim _{s → a+} f (s) = + ∞;
At Point ‘a’ the given function f (s) may or may not be defined and at point x = s the value does not affect the asymptote.
Let’s see the example: let a function f (s) is given:
F (s) = 1 / s if the value of s > 0;
            5 if the value of s ≤ 0
The given function has a limit of + ∞ as s → 0⁺, the function f (s) has the Vertical Asymptote s = 0, even the value of f (0) = 5. The graph of this function interests the vertical asymptote at point (0, 5).
Horizontal Asymptotes: Horizontal Asymptotes are the horizontal lines in which a graph of a function tends to s → + ∞.
The horizontal line is given by:
⇒s = c; the given equation is a Horizontal Asymptotes of a function s = f (p);
If it satisfy the given equation, and the equation is shown below.
⇒lim _{p → - ∞} f (p) = c or we can write it as:
  
⇒lim _{p → + ∞} f (p) = c.