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Horizontal and Slant (Oblique) Asymptotes

So, let's do this one the quick way:

Find the horizontal asymptote of

f ( x ) = ( x^2 - x - 6 ) / ( x^2 - 1 )

Look atx^2 / x^2 = 1

The horizontal asymptote is the line

y = 1

graph of the asymptote y = 1 ... it is dashed

Now, try another one in your head:




Find the horizontal asymptote of

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

Look at3x^2 / 5x^2

The horizontal asymptote is the line

y = 3/5

TRY IT:

Find the horizontal asymptote of

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