Answer
$\text{Domain: }
(-\infty, \infty)
\\\text{Range: }
(-\infty,2]
$
Work Step by Step
Using a graphing calculator, , the graph of the given function, $f(x)=
-x^2+2x+1
,$ is shown above.
Based on the graph its domain and range are as follows:
\begin{array}{l}\require{cancel}
\text{Domain: }
(-\infty, \infty)
\\\text{Range: }
(-\infty,2]
.\end{array}