\( F(3) = \boxed{0} \)
\( x \) for \( F(x) = -5 \) are \( \boxed{2 - 2i} \) and \( \boxed{2 + 2i} \)
\( x \) for \( F(x) = 1 \) are \( \boxed{2 - \sqrt{2}} \) and \( \boxed{2 + \sqrt{2}} \)
\( F(-7) = \boxed{57} \)
Minimum: \( \boxed{1} \)
Maximum: \( \boxed{\infty} \)
Domain: \( \boxed{(-\infty, \infty)} \)
Range: \( \boxed{[1, \infty)} \)
Function is constant: \( \boxed{\text{none}} \)
Rate of change at \( x = -2 \): \( \boxed{-4} \)
Function is decreasing: \( \boxed{(-\infty, 2)} \)
Function is increasing: \( \boxed{(2, \infty)} \)