32. Describe the transformation of the graph of $g(x)=\sin x$ represented by the equation $f(x)=\frac{1}{2} \sin x+2$

Step 1 ：The function \(f(x)=\frac{1}{2} \sin x+2\) is a transformation of the function \(g(x)=\sin x\).

Step 2 ：The coefficient \(\frac{1}{2}\) in front of the sine function compresses the graph vertically by a factor of \(\frac{1}{2}\). This means the amplitude of the function is halved.

Step 3 ：The constant \(2\) added to the function shifts the graph upwards by \(2\) units. This means the midline of the function is raised to \(y=2\).

Step 4 ：Therefore, the transformation of the graph of \(g(x)=\sin x\) represented by the equation \(f(x)=\frac{1}{2} \sin x+2\) is a vertical compression by a factor of \(\frac{1}{2}\) and a vertical shift upwards by \(2\) units.