# What is the end behavior of f(x)=-3x^5-4x^2+3?

Aug 30, 2017

$f \left(x\right) \rightarrow + \infty \text{ as } x \rightarrow - \infty$
$f \left(x\right) \rightarrow - \infty \text{ as } x \rightarrow + \infty$

#### Explanation:

When dealing with end behavior, only the term with the highest degree is significant (because as $x \rightarrow \pm \infty$ its magnitude will exceed those of all other terms).

As $x \rightarrow - \infty$
$\textcolor{w h i t e}{\text{XXX}} {x}^{5} \rightarrow - \infty$
and
$\textcolor{w h i t e}{\text{XXX}} - 3 {x}^{5} \rightarrow + \infty$

Asw $x \rightarrow + \infty$
$\textcolor{w h i t e}{\text{XXX}} {x}^{5} \rightarrow + \infty$
and
$\textcolor{w h i t e}{\text{XXX}} - 3 {x}^{5} \rightarrow - \infty$