Answer
$$\eqalign{
& {\text{The domain of the function is }}\left[ { - 5,5} \right] \cr
& {\text{The range of the function is }}\left[ { - 1,0} \right] \cr
& {\text{The equation is a function}} \cr} $$
Work Step by Step
$$\eqalign{
& y = - \sqrt {1 - \frac{{{x^2}}}{{25}}} \cr
& {\text{Square each side}} \cr
& {\left( y \right)^2} = {\left( { - \sqrt {1 - \frac{{{x^2}}}{{25}}} } \right)^2} \cr
& {y^2} = 1 - \frac{{{x^2}}}{{25}} \cr
& {\text{Write in standard form}}. \cr
& \frac{{{x^2}}}{{25}} + {y^2} = 1 \cr
& {\text{This is the equation of an ellipse }}\frac{{{x^2}}}{{{a^2}}} + \frac{{{y^2}}}{{{b^2}}} = 1 \cr
& a = 5,\,\,\,\,b = 1 \cr
& {\text{In the original equation}},{\text{ the radical expression}}\,\,\, - \sqrt {1 - \frac{{{x^2}}}{{25}}} \cr
& {\text{represents a negative number, number}},{\text{ so the only possible }} \cr
& {\text{values of }}y{\text{ are negative}} \cr
& {\text{The domain of the function is }}\left[ { - 5,5} \right] \cr
& {\text{The range of the function is }}\left[ { - 1,0} \right] \cr
& {\text{The equation is a function}} \cr
& \cr
& {\text{Graph}} \cr} $$
