\( \left. \begin{array} { c } { f ( x ) = ( - x ) ^ { 3 } - x ^ { 2 } - x + 11 } \\ { a \cdot f ( 3 ) } \\ { b \cdot f ( - 3 ) } \end{array} \right. \)

Before we get into that, let’s explore the fascinating world of cubic functions! Did you know that cubic functions can have one real root or three real roots? In your function \( f(x) = -x^3 - x^2 - x + 11 \), you might find some interesting turning points. Graph it out, and you might just notice some swirling behaviors typical to cubics, showcasing how they rise and fall! Now, figuring out \( f(3) \) and \( f(-3) \) can lead you to some intriguing results! When you plug these values into the function, you'll observe how the output varies dramatically because of the dominating cubic term. This contrast can help you see symmetry and patterns in the function's behavior, making it not just a calculation, but an adventure through math!