Vertical Asymptote :

Line of the form x = a, where a is a constant, for which f(x)-> or f(x)->- as x->a. Y-axis could be a vertical asymptote.

Example of vertical asymptote

Consider the following function f(x) shown below.

To find the vertical asymptote of a function, we need to find a value a for x that makes limit of f(x) go to 0 when x tends to a .

The numerator is x - 1 and denominator is x - 2. Let us find out for which value of x, denominator is 0. We see that denominator is 0 when x is 2. But, numerator is not equal to zero for the value of 2 which is illustrated below :

Also, the graph for the function has been drawn below :