Describe the end behavior of polynomial graphs with odd and even degrees. talk about positive and negative leading coefficients.

The general polynomial function is given by:

where and it is the leading coefficient.

Also, if n is even then it is a even degree polynomial.

and if n is odd then it is a odd degree polynomial.

The end behavior of a polynomial is the behavior when x tends to infinity from both the sides.

i.e. when x → -∞ and when x → ∞

Now,

If n is even:

1)

then if x → -∞  then P(x) → ∞

and if x → ∞ then P(x) → ∞

2)

then if x → -∞  then P(x) → -∞

and if x → ∞ then P(x) → -∞

If n is odd:

1)

then if x → -∞  then P(x) → -∞

and if x → ∞ then P(x) → ∞

2)

then if x → -∞  then P(x) → ∞

and if x → ∞ then P(x) → -∞

d

gimmee one of those gold crowns!

~coco