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

Dec 17, 2016

As $x \to \pm \infty$, $f \left(x\right) \to 2$

#### Explanation:

The end behavior of a function is the behavior of the graph of the function $f \left(x\right)$ as $x$ approaches $+ \infty$ (positive infinity) or $- \infty$ (negative infinity).

As here $f \left(x\right) = - \frac{1}{x} ^ 3 + 2$, as $x \to \infty$, $- \frac{1}{x} ^ 3 \to 0$ and $f \left(x\right) \to 0 + 2 = 2$

and as $x \to - \infty$, $- \frac{1}{x} ^ 3 \to 0$ and $f \left(x\right) \to 0 + 2 = 2$

In between as $x \to 0$, $f \left(x\right) \to \infty$ when $x$ approaches $0$ from positive side and $f \left(x\right) \to - \infty$ when $x$ approaches $0$ from negative side.
graph{-1/x^3+2 [-9.79, 10.21, -2.12, 7.88]}