The graph of $y=\sin (x)$ is vertically stretched by a factor of 3 , shifted a distance of 2 units to the right, and translated 12 units upward. Find a formula for the function whose graph is the resulting graph. \[ f(x)=\square \]

Step 1 ：The question is asking for a transformation of the sine function. The original function is \(y=\sin(x)\). The transformations include a vertical stretch by a factor of 3, a horizontal shift to the right by 2 units, and a vertical shift upwards by 12 units.

Step 2 ：The general form of a transformed sine function is \(y=a\sin(b(x-h))+k\), where \(a\) is the amplitude (vertical stretch or shrink), \(b\) affects the period of the function, \(h\) is the horizontal shift, and \(k\) is the vertical shift.

Step 3 ：In this case, \(a=3\), \(h=2\), and \(k=12\). There is no information given about a change in period or reflection, so \(b=1\).

Step 4 ：Therefore, the function is \(f(x)=3\sin((x-2))+12\).

Step 5 ：\(\boxed{f(x)=3\sin((x-2))+12}\)