ANSWER
[tex]y = \cot(x - \frac{\pi}{3} ) + 2[/tex]
EXPLANATION
The cotangent function that is fully transformed is of the form
[tex]y =a \cot(bx + c) + d[/tex]
where 'a' is the amplitude.
[tex] \frac{\pi}{b} = \pi[/tex]
is the period.
This implies that b=1
The phase shift is
[tex] \frac{c}{b} = - \frac{\pi}{3} [/tex]
Substitute b=1 to get;
[tex]c = - \frac{\pi}{3} [/tex]
and d=2 is the vertical shift.
We choose a=1 to get the required function as
[tex]y = \cot(x - \frac{\pi}{3} ) + 2[/tex]
