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Tail Behavior

Let's look at the other tail:

graph looking at the eventual behavior of the upward tail ... As x gets smaller and smaller, we are following the graph to the left. As we do this, what's happening to the y values on the graph? 53... 725... 9280... 5,932,491 If Pierre was running on this thing, would he need mountain climbing equipment?

As x gets smaller and smaller, the height of the graph is going up, up, up.

As x approaches-infinity, the height of the graph approaches
infinity.  
Asx --> -infinity , f( x ) --> infinity

To sum up:
 

graph of -x^3+ some x stuff ... as x --> -infinity , f( x ) --> infinity ... as x --> infinity , f( x ) --> -infinity