Question

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

Answer 1

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

Explanation:

First, you have to arrange the polynomial by degree

`-5x^3+4x^2-2x+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 `(-5)`.