# How do you find the end behavior of 9x^5 - 8x^3 + 4x?

Feb 9, 2017

See below.

#### Explanation:

The end behaviour of $9 {x}^{5} - 8 {x}^{3} + 4 x$ will be determined by the leading (dominant) term $9 {x}^{5}$.

Ie for $\left\mid x \right\mid \text{>>} 0$, we have $y \approx 9 {x}^{5}$. The right and left ends of this graph (which is of $y = 9 {x}^{5}$) will, therefore, show how the function operates as $x \to \pm \infty$

graph{9x^5 [-3.796, 3.817, -1.905, 1.904]}

The full function looks like this:

graph{9x^5 - 8x^3 + 4x [-3.796, 3.817, -1.905, 1.904]}