Precalculus Review Calculus Preview - Cool math . com - Finding Horizontal and Slant Asymptotes When Graphing Rational Functions

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Coolmath Precalculus Review Calculus Preview
Lesson 18 - Graphing - Rational Functions: Finding Horizontal and Slant Asymptotes (page 5 of 5)
---- This Precalculus review (Calculus preview) lesson explains how to find the horizontal (or slant - oblique) asymptotes when graphing rational functions.

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OK, so what about this one?

f( x ) = ( 3x^3 + 2 ) / ( x^2 - x - 7 )

If we look at		, we find that the		WILL divide in...
But, there's going to be some x stuff left over to deal with. This is when you need to start in with some long division... and we get to ignore the remainder!

( x^2 - x - 7 ) / ( 3x^3 + 0x^2 + 0x + 2 ) ... which gives 3x^3 - 3x^2 - 21x ... subtracting gives 3x^2 + yadda ... The 3x + 3 is the slant asymptote. It's the line y = 3x + 3

You can stop here since the rest will be remainder stuff.

a graph with the slant asymptote y = 3x + 3

TRY IT:

Find the slant asymptote of

f( x ) = ( 5x^2 - 3x + 1 ) / ( x + 2 )

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