Answer:
D. [tex]y=\tan (x-\pi)+2[/tex]
Step-by-step explanation:
We are given the graph of the transformed tangent function.
As, we can see that the graph is shifted 2 units upwards.
That is, the parent function is translated 2 units up.
So, the new function will be of the form, [tex]y=\tan (x)+2[/tex].
Thus, options A and C are not correct.
Moreover, 'If a function f(x) has period P, then the function cf(bx) will have period [tex]\frac{P}{|b|}[/tex].
Also, form the figure, we see that the period of the graphed function is [tex]\pi[/tex].
Since, [tex]y=\tan (x)[/tex] have period [tex]\pi[/tex].
So, function in option B will have period [tex]\frac{\pi}{2}[/tex], which is not possible.
Further, function in option D have period [tex]\pi[/tex].
Thus, the equation of the graphed function is, [tex]y=\tan (x-\pi)+2[/tex].
