Graphing Rational Functions - Cool math Algebra Help Lessons - Finding Horizontal and Slant (Oblique) Asymptotes

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Coolmath Algebra
Graphing Rational Functions Lesson 4 - Horizontal and Slant (Oblique) Asymptotes (page 4 of 4)
---- This algebra lesson explains how to find horizontal and slant (oblique) asymptotes when graphing rational functions.

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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

(which is the x-axis)

This one falls under part

on our list.

YOUR TURN:

Find the horizontal asymptote of

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

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!

( 3x^3 + 0x^2 + 0x + 2 ) / ( x^2 - x - 7 ) = 3x ... this gives 3x^3 - 3x^2 - 21x ... subtract, which gives 3x^2 + yadda ... dividing again gives 3x+ 3 ... this is the slant asymptote ... it's the line y = 3x + 3

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

graph of the slant asymptote y = 3x + 3 ... it is dashed the crosses the y-axis at y = 3 and the x-axis at x = -1

TRY IT:

Find the slant asymptote of

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