Question

Which of the following is the graph of y=sin(4(x-pi))?

Answer 1

Graph A

Explanation:

We are given the graphs for the function
`y=\sin (4(x-\pi ))`.

Now, if a function f(x) has period P, then the function a×f(bx+c)+d will have period
`(P)/(|b|)`.

Since, we can rewrite
`y=\sin (4(x-\pi ))` as
`y=\sin (4x-4\pi)`.

Also, the period of
`\sin x` is
`2\pi`, then period of
`y=\sin (4x-4\pi)` is
`(2\pi)/(4)` i.e.
`(\pi)/(2)`.

Thus, we get that the graph of
`y=\sin (4(x-\pi ))` will repeat after every
`(\pi)/(2)`.

Hence, according to the options, graph A is the correct representation of the function
`y=\sin (4(x-\pi ))`.

Answer 2

we have that
y=sin(4(x-pi))

using a graph tool
see the attached figure

the solution in the attached figure