Answer
$a.$
Since $g(x)=f(x+2)-2$, we start with the graph of f(x) and
- shift it to the left by 2 units ... to get $f(x+2)$
- and lower it by $2$ units ... to get $f(x+2) -2$.
$b.$
Since $g(x)=f(x-2)+2$, we start with the graph of f(x) and
- shift it to the right by 2 units ... to get $f(x-2)$
- and raise it up by $2$ units ... to get $f(x-2)+2$.
Work Step by Step
The exercise is to describe transformations,
so the answer is given in step-by-step form.