# What is end behavior?

Sep 10, 2015

"end behavior" (when applied to a function) is the nature of the value as the function argument approaches $+ \infty$ and $- \infty$

#### Explanation:

For example:

[1] The end behavior of $f \left(x\right) = {x}^{2}$
is $f \left(x\right) \rightarrow + \infty$ (as $x \rightarrow \pm \infty$)

[2] The end behavior of $g \left(x\right) = \frac{1}{x} + 27$
is $g \left(x\right) \rightarrow 27$ (as $x \rightarrow \pm \infty$)

[3] The end behavior of $h \left(x\right) = {x}^{3}$
is $h \left(x\right) \rightarrow + \infty \text{ as } x \rightarrow + \infty$
and $h \left(x\right) \rightarrow - \infty \text{ as } x \rightarrow - \infty$

[4]The end behavior of $i \left(x\right) = \cos \left(x\right)$
is $i \left(x\right)$ oscillates between $+ 1$ and $- 1$ (as $x \rightarrow \pm \infty$)