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 $-7x^3$.
The degree is odd and the coefficient is negative.
Therefore the end behavior of the graph of the given function is up and down.