You confused the graph of $\displaystyle{f{{\left({x}\right)}}}=\sqrt{{x}}-{4}\usepackage{cmbright}\Huge\$ with the graph of $\displaystyle{f{{\left({x}\right)}}}=\sqrt{{{x}-{4}}}\usepackage{cmbright}\Huge\$ (shown in this answer). Subtracting 4 on the inside of the radical moves the graph to the right. Subtracting 4 on the outside moves the graph down from the graph of $\displaystyle\sqrt{{x}}\usepackage{cmbright}\Huge\$ .