Write an Equation for the Function That Is Described by the Given

Multiple Choice

Write an equation for the function that is described by the given characteristics. A sine curve with a period of $4 \pi$ , an amplitude of 8 , a left phase shift of $\frac { \pi } { 4 }$ , and a vertical translation down 1 unit.

A) $y = 8 \sin \left( \frac { x } { 2 } + \frac { \pi } { 8 } \right) - 1$
B) $y = 1 \sin \left( \frac { x } { 2 } + \frac { \pi } { 8 } \right) - 8$
C) $y = 8 \sin \left( \frac { x } { 2 } + \pi \right) - 1$
D) $y = 8 \sin \left( x + \frac { \pi } { 2 } \right) - 1$
E) $y = 8 \sin \left( \frac { x } { 2 } + \frac { \pi } { 8 } \right) + 1$