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Rational Functions - Vertical Asymptotes

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 )