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Rational Functions - Horizontal Asymptotes (and Slants)

TRY IT:

Find the horizontal asymptote of

f( x ) = ( 2x^2 - x + 6 ) / ( 9 - 2x - x^2 )

What about this one?

Find the horizontal asymptote of f( x ) = 2x / ( x^2 - 5x - 3 )
 
Look at 2x / x^2 ... The denominator goes into the numerator 0 times!


So, the horizontal asymptote is the line

y = 0
(which is the x-axis)

This one falls under part 1 on our list.

   

YOUR TURN:

Find the horizontal asymptote of

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