f(x)=-x^3 + 3x^2 + x - 3. using the end - behavior of f(x), determine the graph of the function.

Explanation:

Step1: Identify the degree and leading - coefficient

The function is (f(x)=-x^{3}+3x^{2}+x - 3), the degree (n = 3) (odd) and the leading - coefficient (a=-1) (negative).

Step2: Determine end - behavior rules

For a polynomial function (y = a x^{n}) with (n) odd and (a<0), as (x\to+\infty), (y\to-\infty) and as (x\to-\infty), (y\to+\infty).

Step3: Match with the graphs

Graph W shows that as (x\to+\infty), the function value goes down ((y\to-\infty)) and as (x\to-\infty), the function value goes up ((y\to+\infty)).

Answer:

W