Answer
a) Shift the graph of $f$ one unit downwards
b) Shift the graph of $f$ two units to the right.
Work Step by Step
$a)$ $f(x)-1$
The graph of this function can be obtained by shifting the graph of $f$ one unit downwards.
$b)$ $f(x-2)$
The graph of this function can be obtained by shifting the graph of $f$ two units to the right.