The horizontal shift of the function $f ( x ) = 3 + \sin ( 2 x - \pi )$ is

A)units to the left $\frac { \pi } { 2 }$
B)units to the right $\frac { \pi } { 2 }$
C)units to the left $\pi$
D)units to the right $\pi$
E)units to the left $\frac { \pi } { 8 }$

Question

The horizontal shift of the function $f ( x ) = 3 + \sin ( 2 x - \pi )$ is

A)units to the left $\frac { \pi } { 2 }$
B)units to the right $\frac { \pi } { 2 }$
C)units to the left $\pi$
D)units to the right $\pi$
E)units to the left $\frac { \pi } { 8 }$

Quizplus · Accepted Answer

The horizontal shift is determined by the phase shift in the sine function, which is given by the formula $\frac{C}{B}$ when the function is in the form $\sin(Bx - C)$. Here, $B = 2$ and $C = \pi$, so the phase shift is $\frac{\pi}{2}$ to the right, because the sign inside the parentheses is negative, indicating a rightward shift.

The Horizontal Shift of the Function f(x)=3+sin⁡(2x−π)f ( x ) = 3 + \sin ( 2 x - \pi )f(x)=3+sin(2x−π)

The Horizontal Shift of the Function $f ( x ) = 3 + \sin ( 2 x - \pi )$