What is the end behavior of #f(x)=-x^6+2x^3-x#?

1 Answer
SoySoy4444
Dec 11, 2017

Approaches #-oo#

Explanation:

As #x# becomes infinitely large, the term with the highest exponent dominates the expression. In this case, it is the #-x^6#.

We only need to look at what happens to the #-x^6#.

As #x# increases, #y# decreases and this continues infinitely.
Therefore, the end behaviour of #f(x)# is that it approaches #-oo#

Here is the graph of this function.
graph{-x^6+2x^3-x [-7.023, 7.024, -3.51, 3.513]}

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