Answer
(a) See graph (red curve).
(b) domain $(-\infty,\infty)$, range $[-9,\infty)$.
(c) decreasing on $(-\infty,1)$, increasing on $(1,\infty)$.
Work Step by Step
(a) To graph $y=x^2-2x-8=(x-1)^2-9$, start from $y=x^2$, shift the curve 1 unit(s) to the right, then shift 9 units down. See graph (red curve).
(b) We can determine the domain $(-\infty,\infty)$, range $[-9,\infty)$.
(c) The function is decreasing on $(-\infty,1)$, increasing on $(1,\infty)$.
