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Coolmath Precalculus Review Calculus Preview
Lesson 14 - Graphing - Tail Behavior (Intro to Limits at Infinity)
(page 4 of 4)

---- This Precalculus review (Calculus preview) lesson explores what happens with the tails of polynomials - this is really an introduction to limits at infinity.

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Let's do another one:

f( x ) = x^4 + some x stuff
 

graph of f( x ) = x^4 + some x stuff  ...  as x  -->  -infinity  ,  f( x )  -->  infinity  ...  as x  --> infinity  ,  f( x )  -->  infinity
 

Both tails are shooting up on this guy.  So, whether Pierre runs way out to the right or to the left, it's mountain climbing time.

Yes, Pierre will be sporting lederhosen.

What about this one?

f( x ) = x^5 + some x stuff

graph of f( x ) = x^5 + some x stuff  ...  as x  -->  -infinity  ,  f( x )  -->  -infinity  ...  as x   -->  infinity  ,  f( x )  -->  infinity

 


TRY IT:

Draw a rough sketch of the graphs and label the end-tail behavior:
 

f( x ) = -x^6 + some x stuff
 

f( x ) = -x^5 + some x stuff


FYI, what we've been doing here is called "finding limits"...  And, yes, this is Calculus, baby!  Not bad, eh?

 The printing and distribution and/or downloading of these lessons is strictly prohibited.

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