# How do you describe the end behavior for f(x)=x^3+10x^2+32x+34?

May 31, 2018

${\lim}_{x \to \infty} f \left(x\right) = \infty , {\lim}_{x \to - \infty} f \left(x\right) = - \infty$

#### Explanation:

To find the end behavior of this function, we can evaluate its limits at positive and negative infinity.

In $f \left(x\right)$, the term with the highest exponent will dominate the end behavior, so we can evaluate the limit of those. We have

${\lim}_{x \to \infty} {x}^{3} = \infty$

As $x$ gets very large, the exponent will just make it balloon. The value will stay positive.

${\lim}_{x \to - \infty} {x}^{3} = - \infty$

As $x$ gets very negative, the function will go towards negative infinity, because of the odd exponent.

Hope this helps!