Answer
(a) See graph (red curve).
(b) domain $(-\infty,\infty)$, range $(-\infty,2]$.
(c) increasing on $(-\infty,3)$, decreasing on $(3,\infty)$.
Work Step by Step
(a) To graph $y=-2(x-3)^2+2$, start from $y=x^2$, shift the curve 3 unit(s) to the right, stretch vertically by a factor of 2, reflect across the x-axis, then shift 2 unit(s) up. See graph (red curve).
(b) We can determine the domain $(-\infty,\infty)$, range $(-\infty,2]$.
(c) The function is increasing on $(-\infty,3)$, decreasing on $(3,\infty)$.
