Asymptote

An Asymptote is basically a line in which a graph approaches, but it never intersects the line. For example: In the following given graph of P =1 / Q, (here the x axis is denoted by ‘P’ and y axis is denoted by Q) the line approaches the p-axis (Q=0), but the line never touches it. The line can reach to infinity but it never touch. The line will not actually reach Q = 0, but will always get closer and closer.
  
It means the line Q = 0 is along to the Horizontal Asymptote. Horizontal asymptotes arise mostly when the given function is a fraction where the top part remains positive, but the bottom part goes to infinity. We will see in the example that the value Q = 1 / P is a fraction. If we find the infinity on the x-axis then the top of the fraction remains 1, but the bottom fraction gets bigger and bigger. As a result we can say that the entire fraction actually gets smaller, although it will not be zero. The function will be 1/2, then 1/3, then 1/10, even 1/10000, but never quite 0. Thus, Q = 0 is a horizontal asymptote for the function y = 1 / p. this is how to define asymptote.
Now we will see some types of asymptote which are mention below:
Vertical asymptote and Horizontal asymptote:
Let’s have a small introduction about Horizontal asymptotes.
Horizontal Asymptotes: Horizontal Asymptotes are the horizontal lines in which the graph of the function tends to x → + ∞.
The horizontal line is given by:
⇒u = c; the given equation is a Horizontal Asymptotes of a function u = 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.
This is the asymptote definition.