Answer
Domain: $(-\infty ,\infty)$
Range: $( -\infty, 7]$
Work Step by Step
Given $$ f(x) = -2(x-3)^2+7.$$ Student's work:
Domain: $(-\infty ,\infty)$.
Range: $ (7,\infty )$.
The domain is correct. The range indicates that the parabola faces upward, and the parenthesis on the $7$ should be a bracket. The correct answer is
Domain: $(-\infty ,\infty)$
Range: $( -\infty, 7]$.
