OK, so for vertical asymptotes...

Set the denominator = 0 and solve.

This is like finding the bad spots in the domain.  It's where the function cannot exist.
 

Check it out:

f( x ) = ( x^2 - x - 6 ) / ( x^2 - 1 ) denominator = 0  ...  x^2 - 1 = 0  ...  ( x - 1 )( x + 1 ) = 0  ...  x - 1 = 0  or  x + 1 = 0  ...  x = 1  ,  x = -1

 

So, the vertical asymptotes are the lines

x = 1 and x = -1
 

They look like

a graph with vertical asymptotes at x = -1 and x = 1

 

We draw them with dashes since they are really invisible.

 


TRY IT:

Find (and draw) the vertical asymptotes of

f( x ) = ( x - 3 ) / ( x^2 - 3x - 10 )