Chapter 2 - Functions and Their Graphs - 2.5 Graphing Techniques: Transformations - 2.5 Assess Your Understanding - Page 103: 28

$g(x)=-\sqrt {x-3}-2$

Let the final function be $g(x)$. Start from $f(x)=\sqrt x$ (1) Reflect about the x-axis gives $-f(x)$ (2) Shift right 3 units gives $-f(x-3)$ (3) Shift down 2 units gives $-f(x-3)-2$. Thus the function is $g(x)=-\sqrt {x-3}-2$.