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Tail Behavior

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?