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

1 Answer
Nov 2, 2017

Answer:

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)#.