#### Answer

The leading term has:
degree: odd
leading coefficient: negative
Therefore the end behavior of the graph is:
$\underline{\text{up and down}}$

#### Work Step by Step

RECALL:
The end behavior of the graph of a polynomial function is dependent on its leading term $ax^n$ and its degree $n$.
(i) If the leading term's degree is even:
(a) the end behavior is up and up if the leading coefficient is positive and
(b) the end behavior is down and down if the leading coefficient is negative.
(ii) If the leading term's degree is odd:
(a) the end behavior is down and up if the leading coefficient is positive and
(b) the end behavior is up and down if the leading coefficient is negative.
The leading term of the given function is $-4x^9$.
The degree is odd and the coefficient is negative.
Therefore the end behavior of the graph of the given function is up and down.