How do you determine the end behavior of f(x)=6-2x+4x^2-5x^3?

Nov 2, 2017

Opposite tails (up to down as you go from left to right).

Explanation:

First, you have to arrange the polynomial by degree

$- 5 {x}^{3} + 4 {x}^{2} - 2 x + 6$

then you can see that $- 5$ is the leading coefficient and that $3$ is the highest degree, these two attributes tell you the end behavior.

The degree tells you if the tails go in opposite directions (odd degree) or the same direction (even degree). $3$ is an odd number so the tails go in the opposite direction, and the function goes from up to down because the leading coefficient is negative $\left(- 5\right)$.