Answer:
D. [tex]\text{Period}=\frac{\pi}{2}[/tex]; Phase shift [tex]x=\frac{\pi}{2}[/tex]
Step-by-step explanation:
We have been given a function [tex]f(x)=5\text{ tan}(2x-\pi)[/tex]. We are asked to find the period and phase shift for the given function.
We will use formula [tex]f(x)=a\cdot \text{tan}(bx-c)+d[/tex], where,
a = Amplitude,
[tex]\text{Period}=\frac{\pi}{|b|}[/tex]
[tex]\text{Phase shift}=\frac{c}{b}[/tex]
d = Vertical shift.
Upon substituting the given values we will get period of the given function as:
[tex]\text{Period}=\frac{\pi}{|2|}=\frac{\pi}{2}[/tex]
We can find phase shift for our given function as:
[tex]x=\frac{\pi}{2}[/tex]
Therefore, option D is the correct choice.
