f(x) = \begin{cases}
-x^3 - 2 x^2 - 2 x - 7, & x < -3\\
-x^3 - 4 x^2 - 4 x + 5, & -3 \leq x < -1 \\
x^3 + 2 x^2 + 2 x + 7, & -1 \leq x < 2 \\
x^3 + 4 x^2 + 4 x - 5, & x \geq 2
\end{cases}