Answer:
Graph A
Step-by-step explanation:
We are given the graphs for the function [tex]y=\sin (4(x-\pi ))[/tex].
Now, if a function f(x) has period P, then the function a×f(bx+c)+d will have period [tex]\frac{P}{|b|}[/tex].
Since, we can rewrite [tex]y=\sin (4(x-\pi ))[/tex] as [tex]y=\sin (4x-4\pi)[/tex].
Also, the period of [tex]\sin x[/tex] is [tex]2\pi[/tex], then period of [tex]y=\sin (4x-4\pi)[/tex] is [tex]\frac{2\pi}{4}[/tex] i.e. [tex]\frac{\pi}{2}[/tex].
Thus, we get that the graph of [tex]y=\sin (4(x-\pi ))[/tex] will repeat after every [tex]\frac{\pi}{2}[/tex].
Hence, according to the options, graph A is the correct representation of the function [tex]y=\sin (4(x-\pi ))[/tex].
