Chapter 2 - Functions and Their Graphs - 2.5 Graphing Techniques: Transformations - 2.5 Assess Your Understanding - Page 103: 29

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

Let the final function be $g(x)$. Start from $f(x)=\sqrt x$ (1) Reflecting about the $x$-axis gives $-f(x)$. (2) Shifting up $2$ units yields $-f(x)+2$. (3) Shifting left $3$ units gives $-f(x+3)+2$. Thus, $g(x)= -\sqrt {x+3}+2$.