Module 4 : Local / Global Maximum / Minimum and  Curve Sketching
Lecture 12 : Asymptoes [Section 12.1]
  This motivates our next definition.
12.1.2 Definitions:
  Let and be a real valued function defined on .
(i)
 A line is called a horizontal asymptote on the left to if
                             
  In other words, the graph of approaches the line as we keep moving to the left on the -axis.
(ii)
 A line is called a horizontal asymptote on the right to if
                                .
In other words, the graph of approaches the line as we keep moving to the right on the -axis.

(iii)
 A line is called a vertical asymptote from left at to if
 

                             
i.e., the function approaches the vertical line as approaches the point from the left on the
-axis.

(iv)
 A line is called a vertical asymptote from right at to if
 

                            ,
i.e., the function approaches the vertical line as approaches the point the right on the -axis.

1
3