You confused the graph of $\displaystyle{f{{\left({x}\right)}}}=-{3}-\sqrt{{x}}\usepackage{cmbright}\Huge\$ with the graph of $\displaystyle{f{{\left({x}\right)}}}=\sqrt{{{x}-{3}}}\usepackage{cmbright}\Huge\$ (shown in this answer). When you multiply the radical by a negative number, the direction of the graph changes, because the function decreases as x increases. So the real graph is going down.