# How do you describe the end behavior of f(x)=x^5-4x^3+5x+2?

Nov 8, 2017

See below.

#### Explanation:

For end behaviour of a polynomial we only need to be concerned with the degree and leading coefficient as we approach $\infty$ and $- \infty$

For this example the degree is 5 and leading coefficient is 1.

as $x \to \infty$ , ${x}^{5} \to \infty$

as $x \to - \infty$ , ${x}^{5} \to - \infty$

(a negative value raised to an odd power is always negative )

So range of function is:

$\left[y \in \mathbb{R}\right\}$

Graph: graph{x^5-4x^3+5x+2 [-14.24, 14.24, -7.12, 7.13]}