Answer
See graph:
(a) $(2,-1)$.
(b) $x=2$.
(c) $(-\infty,\infty)$.
(d) $[-1,\infty)$.
(e) $(2,\infty)$.
( f ) $(-\infty,2)$.
Work Step by Step
See graph:
(a) Given $f(x)=\frac{2}{3}x^2-\frac{8}{3}x+\frac{5}{3}=\frac{2}{3}(x^2-4x+4)-1=\frac{2}{3}(x-2)^2-1$, 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 $[-1,\infty)$.
(e) the largest open interval of the domain over which the function is increasing can be identified as $(2,\infty)$.
( f ) the largest open interval over which the function is decreasing can be identified as $(-\infty,2)$.
