Question

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

Answer 1

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]}