Question

How do you describe the end behavior of `f(x)=-1/x^3+2`?

Answer 1

As `x->+-oo`, `f(x)->2`

Explanation:

The end behavior of a function is the behavior of the graph of the function `f(x)` as `x` approaches `+oo` (positive infinity) or `-oo` (negative infinity).

As here `f(x)=-1/x^3+2`, as `x->oo`, `-1/x^3->0` and `f(x)->0+2=2`

and as `x->-oo`, `-1/x^3->0` and `f(x)->0+2=2`

In between as `x->0`, `f(x)->oo` when `x` approaches `0` from positive side and `f(x)->-oo` when `x` approaches `0` from negative side.
graph{-1/x^3+2 [-9.79, 10.21, -2.12, 7.88]}