Final answer:
The end behavior of the given polynomial function is downward on both sides.
Step-by-step explanation:
The end behavior of a polynomial function is determined by the highest power of x in the function. In this case, the highest power of x is 3 (from the term x(2x+1)(x+2)).
When the degree of a polynomial is odd, the end behavior is either upward on both sides or downward on both sides. Since the degree of this polynomial is odd, the end behavior will be the same on both sides. If the leading coefficient is positive, the end behavior is upward, and if the leading coefficient is negative, the end behavior is downward.
Therefore, the end behavior of the given polynomial function f(x)=-x(2x+1)(x+2) is downward on both sides because the leading coefficient (-1) is negative.