Answer
See graph:
(a) $(5,-4)$.
(b) $x=5$.
(c) $(-\infty,\infty)$.
(d) $[-4,\infty)$.
(e) $(5,\infty)$.
( f ) $(-\infty,5)$.
Work Step by Step
See graph:
(a) Given $f(x)=(x-5)^2-4$, we can find its vertex at $(5,-4)$.
(b) The axis can be found as $x=5$.
(c) The domain can be found as $(-\infty,\infty)$.
(d) The range can be found as $[-4,\infty)$.
(e) the largest open interval of the domain over which the function is increasing can be identified as $(5,\infty)$.
( f ) the largest open interval over which the function is decreasing can be identified as $(-\infty,5)$.