Answer
a) $g(x)=\sqrt {x+1}-7$
b) $g(x)=-\sqrt{-x+3}-4$
Work Step by Step
a) We start with the graph of the function $f(x)=\sqrt x$.
Horizontally shift $f(x)$ one unit to the left to get $a(x)=\sqrt {x+1}$.
Vertically shift $a(x)$ seven units downward to get the function from the given graph:
$g(x)=\sqrt {x+1}-7$
b) We start with the graph of the function $f(x)=\sqrt x$.
Reflect $f(x)$ across the $y$-axis to get $a(x)=\sqrt {-x}$.
Reflect $a(x)$ across the $x$-axis to get $b(x)=-\sqrt {-x}$.
Horizontally shift $b(x)$ three units to the right to get $c(x)=-\sqrt{-x+3}$.
Finally, vertically shift $c(x)$ four units downward to get the function from the given graph:
$g(x)=-\sqrt{-x+3}-4$
