(b)We are starting with the parent function \(\displaystyle{f{{\left({x}\right)}}}={x}^{{3}}\)

STEP 1: Shift the graph hy 2 units to the right, to get \(\displaystyle{y}={\left({x}-{2}\right)}^{{3}}\)

STEP 2: Shift the graph hy 2 units upwards, to get \(\displaystyle{y}={\left({\left({x}-{2}\right)}^{{3}}\right)}+{2}\), which is the required function h(x) Shift the graph by 2 units the right and 2 units upwards

STEP 1: Shift the graph hy 2 units to the right, to get \(\displaystyle{y}={\left({x}-{2}\right)}^{{3}}\)

STEP 2: Shift the graph hy 2 units upwards, to get \(\displaystyle{y}={\left({\left({x}-{2}\right)}^{{3}}\right)}+{2}\), which is the required function h(x) Shift the graph by 2 units the right and 2 units upwards