We are starting with the parent function \(f(x)=|x|\)

STEP 1:

Vertically compress the graph by a factor of \(\frac{1}{2}\), to get \(y=\frac{1}{2}|x|\)

STEP 2:

Shift the graph by 2 units to the right, to get \(y=\frac{1}{2}|x-2|\)

STEP 3:

Shift the graph by 3 units downwards, to get \(y=\frac{1}{2}|x-2|-3\), which is the required function g(x)