We are starting with the parent function \(\displaystyle{f{{\left({x}\right)}}}={x}^{{2}}\)

SETP 1: Vertically compress the graph by a factor of 2/3, to get \(\displaystyle{y}={\left(\frac{{2}}{{3}}\right)}{x}^{{2}}\)

STEP 2: Shift the graph by 4 units up, to get \(\displaystyle{y}={\left(\frac{{2}}{{3}}\right)}{x}^{{2}}+{4}\), which is the required function g(x)

SETP 1: Vertically compress the graph by a factor of 2/3, to get \(\displaystyle{y}={\left(\frac{{2}}{{3}}\right)}{x}^{{2}}\)

STEP 2: Shift the graph by 4 units up, to get \(\displaystyle{y}={\left(\frac{{2}}{{3}}\right)}{x}^{{2}}+{4}\), which is the required function g(x)