Chapter 2 - Functions and Their Graphs - 2.5 Graphing Techniques: Transformations - 2.5 Assess Your Understanding - Page 103: 30

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

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