Answer
See graph:
(a) $(4,2)$.
(b) $x=4$.
(c) $(-\infty,\infty)$.
(d) $(-\infty,2]$.
(e) $(-\infty,4)$.
( f ) $(4,\infty)$.
Work Step by Step
See graph:
(a) Given $f(x)=-3x^2+24x-46=-3(x^2-8x+16)+2=-3(x-4)^2+2$, we can find its vertex at $(4,2)$.
(b) The axis can be found as $x=4$.
(c) The domain can be found as $(-\infty,\infty)$.
(d) The range can be found as $(-\infty,2]$.
(e) the largest open interval of the domain over which the function is increasing can be identified as $(-\infty,4)$.
( f ) the largest open interval over which the function is decreasing can be identified as $(4,\infty)$.