(a) The function \(f(x) = 2 - 3 \sin 2x\) has a range determined by the values of \(\sin 2x\), which varies from \(-1\) to \(1\). Therefore, \(f(x)\) ranges from \(2 - 3(1) = -1\) to \(2 - 3(-1) = 5\).

The function \(g(x) = -2f(x)\) will have a range that is twice the range of \(f(x)\) and inverted. Thus, \(g(x)\) ranges from \(-2(5) = -10\) to \(-2(-1) = 2\).

(b) The graph of \(y = g(x)\) is a reflection of \(y = f(x)\) in the x-axis and stretched by a factor of 2 in the y direction.

(c) To map \(y = f(x)\) onto \(y = h(x)\), perform the following transformations:

• Reflect in the x-axis.
• Stretch by a factor of 2 in the y direction.
• Translate by \(-\pi\) in the x direction, or equivalently, translate by \(\begin{pmatrix} 0 \\ -\pi \end{pmatrix}\).