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Rational Functions - Horizontal Asymptotes (and Slants)

So, let's do this one the quick way:
Find the horizontal asymptote off( x ) = ( x^2 - x - 6 ) / ( x^2 - 1 )

 

Look atx^2 / x^2 = 1

The horizontal asymptote is the line

y = 1
 

graph with a horizontal asymptote at y = 1

 

Now, try another one in your head:

 


Find the horizontal asymptote of

f( x ) = ( x + 3x^2 ) / ( 5x^2 - 6x - 1 ) ... the x^2 is the king of the top
 
Look at3x^2 / 5x^2


The horizontal asymptote is the line

y = ( 3 / 5 )