Answer:
Last Option moved [tex]\frac{\pi}{2}[/tex] units right
Step-by-step explanation:
If we have a function f(x) and we want to move it horizontally then we make the transformation:
[tex]y = f (x + h)[/tex]
If [tex]h <0[/tex] then the graph of f(x) moves horizontally h units to the right
If [tex]h> 0[/tex] then the graph of f(x) moves horizontally h units to the left.
In this case we have the function [tex]y = tan (x)[/tex] and the transformation is performed to obtain [tex]y = tan(x- \frac{\pi}{2})[/tex]
Notice that in this transformation
[tex]h <0 = -\frac{\pi}{2}[/tex]
Then the graph of [tex]y = tan (x)[/tex] moves horizontally [tex]\frac{\pi}{2}[/tex] to the right
