Sketching Polynomial Functions

End behavior is the behavior of the graph of $f(x)$ as $x$ approaches positive or negative infinity. Let's consider the given graph.

We can see above that as $x$ approaches negative infinity, $f(x)$ approaches positive infinity. As $x$ approaches positive infinity, $f(x)$ approaches negative infinity. $$\begin{array}{c}f(x)\to +\infty \text{ as }x\to \text{-}\infty \\ \text{and}\\ f(x)\to \text{-}\infty \text{ as }x\to +\infty \end{array}$$