To transform the graph of \(y = \sin x\) to \(y = f(x) = 3 + 2 \sin \frac{1}{4}x\), apply the following transformations in order:

1. Stretch the graph horizontally by a factor of 4 in the x-direction. This changes \(\sin x\) to \(\sin \frac{1}{4}x\).

2. Stretch the graph vertically by a factor of 2 in the y-direction. This changes \(\sin \frac{1}{4}x\) to \(2 \sin \frac{1}{4}x\).

3. Translate the graph vertically by 3 units upwards. This changes \(2 \sin \frac{1}{4}x\) to \(3 + 2 \sin \frac{1}{4}x\).