How do you find the end behavior of #y = -x^4+3x^3-3x^2+6x+8#?

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Answer 1 · 2015-05-03T16:02:13

The end behavior of a function is the behavior of the function as x approaches positive infinity or negative infinity.

So we have to do these two limits:

#lim_(xrarr-oo)f(x)#

and

#lim_(xrarr+oo)f(x)#.

Than:

#lim_(xrarr-oo)(-x^4+3x^3-3x^2+6x+8)=lim_(xrarr-oo)(-x^4)=-oo#

and

#lim_(xrarr+oo)(-x^4+3x^3-3x^2+6x+8)=lim_(xrarr+oo)(-x^4)=-oo#.

This is because the power #-x^4# is the highest power and its behavior is the same of the whole function.