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.

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