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Tail Behavior

Look at this graph:

y = -x^3 + some x stuffa possible graph of y = -x^3 + some x stuff

Remember that this guy goes on forever.  That's what those arrows are for!

graph looking at the eventual behavior of the downward tail ... As x gets bigger and bigger, we are following the graph way out to the right. As we do this, what happens to the y values on the graph? Thiink about it. They get smaller and smaller. -100... -5360... -2,524,791 If Pierre was running on this thing, would he need some serious scuba diving equipment?

As x gets bigger and bigger, the height of the graph is going down, down, down!

To get a little math notation going...

As

 

This little arrow can be read as "approaches" or "goes to."

And remember that f(x) is just a fancy name for y...

As