end behavior

the end behavior of a function $f(x)$ is the limit of $f(x)$ as $x$ approaches negative infinity, $\underset{x\to -\infty }{\lim }f(x)$, and positive infinity, $\underset{x\to \infty }{\lim }f(x)$
in simple terms, the value of the graph of $f(x)$ when you look towards the left and the right