Answer
See graph:
(a) $(1,3)$.
(b) $x=1$.
(c) $(-\infty,\infty)$.
(d) $[3,\infty)$.
(e) $(1,\infty)$.
( f ) $(-\infty,1)$.
Work Step by Step
See graph:
(a) Given $f(x)=2x^2-4x+5=2(x^2-2x+1)+3=2(x-1)^2+3$, we can find its vertex at $(1,3)$.
(b) The axis can be found as $x=1$.
(c) The domain can be found as $(-\infty,\infty)$.
(d) The range can be found as $[3,\infty)$.
(e) the largest open interval of the domain over which the function is increasing can be identified as $(1,\infty)$.
( f ) the largest open interval over which the function is decreasing can be identified as $(-\infty,1)$.
