Answer
a) $g(x)=-|x+3|$
b) $g(x)=|x-2|-4$
Work Step by Step
a) We start with the graph of the function $f(x)=|x|$.
Reflect $f(x)$ across the $x$-axis to get $a(x)=-|x|$.
Horizontally shift $a(x)$ three units to the left to get the function from the given graph:
$g(x)=-|x+3|$
b) We start with the graph of the function $f(x)=|x|$.
Horizontally shift $f(x)$ two units to the right to get $a(x)=|x-2|$.
Finally, vertically shift $a(x)$ four units downward to get the function from the given graph:
$g(x)=|x-2|-4$
