Answer
$\text{Domain: }
(-\infty,\infty)
\\\text{Range: }
(-\infty,4)$
See graph.
Work Step by Step
The red graph is the graph of the first piece.
The blue graph is the graph of the second piece.
The graph of the given piecewise function, $
f(x)=
\begin{cases}
4x-4
\text{ if }
x\lt2
\\
-x+1
\text{ if }
x\ge2
,\end{cases}$
is shown above.
Based on the graph, then
\begin{array}{l}\require{cancel}
\text{Domain: }
(-\infty,\infty)
\\\text{Range: }
(-\infty,4)
.\end{array}