Answer
$$\eqalign{
& {\text{domain: }}\left[ { - 5,3} \right] \cr
& {\text{range: }}\left[ { - 3,5} \right] \cr} $$
Work Step by Step
$$\eqalign{
& \frac{{{{\left( {x + 1} \right)}^2}}}{{16}} + \frac{{{{\left( {y - 1} \right)}^2}}}{{16}} = 1 \cr
& {\text{Multiply both sides by 16}} \cr
& {\left( {x + 1} \right)^2} + {\left( {y - 1} \right)^2} = 16 \cr
& {\text{The equation is written in the form }}{\left( {x - h} \right)^2} + {\left( {y - k} \right)^2} = {r^2} \cr
& {\left( {x + 1} \right)^2} + {\left( {y - 1} \right)^2} = 16,\,\,\,\,\,\,h = - 1,\,\,\,\,k = 1,\,\,\,\,\,r = 4 \cr
& {\text{This equation represents a circle centered at }}\left( {h,k} \right):\left( { - 1,1} \right) \cr
& {\text{Radius }}r = 4 \cr
& {\text{The domain of the circle is }}\left[ {h - r,h + r} \right] \cr
& {\text{domain: }}\left[ { - 5,3} \right] \cr
& {\text{The range of the circle is }}\left[ {k - r,k + r} \right] \cr
& {\text{range: }}\left[ { - 3,5} \right] \cr
& \cr
& {\text{Therefore,}} \cr
& {\text{domain: }}\left[ { - 5,3} \right] \cr
& {\text{range: }}\left[ { - 3,5} \right] \cr
& \cr
& {\text{Graph}} \cr} $$
