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

Dec 11, 2017

Approaches $- \infty$

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 $f \left(x\right)$ is that it approaches $- \infty$

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