Answer
(a) See graph (red curve).
(b) domain $(-\infty,\infty)$, range $(-\infty,4]$.
(c) increasing on $(-\infty,-1)$, decreasing on $(-1,\infty)$.
Work Step by Step
(a) To graph $y=-3(x+1)^2+4$, start from $y=x^2$, shift the curve 1 unit(s) to the left, stretch vertically by a factor of 3, reflect across the x-axis, then shift 4 unit(s) up. See graph (red curve).
(b) We can determine the domain $(-\infty,\infty)$, range $(-\infty,4]$.
(c) The function is increasing on $(-\infty,-1)$, decreasing on $(-1,\infty)$.
