Answer
See graph:
(a) $(2,1)$.
(b) $x=2$.
(c) $(-\infty,\infty)$.
(d) $(-\infty, 1]$.
(e) $(-\infty,2)$.
( f ) $(2,\infty)$.
Work Step by Step
See graph:
(a) Given $f(x)=-3(x-2)^2+1$, we can find its vertex at $(2,1)$.
(b) The axis can be found as $x=2$.
(c) The domain can be found as $(-\infty,\infty)$.
(d) The range can be found as $(-\infty, 1]$.
(e) the largest open interval of the domain over which the function is increasing can be identified as $(-\infty,2)$.
( f ) the largest open interval over which the function is decreasing can be identified as $(2,\infty)$.