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 4, a left phase shift of $\frac { \pi } { 4 }$ , and a vertical translation down 5 units.

A) $y = 4 \sin \left( x + \frac { \pi } { 8 } \right) - 5$
B) $y = 4 \sin \left( \frac { x } { 2 } + \frac { \pi } { 8 } \right) + 5$
C) $y = 4 \sin \left( \frac { x } { 2 } + \frac { \pi } { 8 } \right) - 5$
D) $y = 4 \sin \left( \frac { x } { 2 } + \pi \right) - 5$
E) $y = 5 \sin \left( \frac { x } { 2 } + \frac { \pi } { 8 } \right) - 4$