Final answer:
The function y = -4 - 2sin[5xπ/4] has been translated downward by 4 units. The constant term -4 indicates the vertical translation. Option number b is correct.
Step-by-step explanation:
The student has asked to find the vertical translation of the function y = -4 - 2sin[5xπ/4]. A vertical translation involves shifting the graph of the function up or down on the y-axis without altering its shape. In the function given, the constant term outside the sine function is -4. This term indicates a vertical translation.
Since vertical translations correspond to the addition or subtraction of a constant to the entire function, and considering that up is the positive direction, the function y = -4 - 2sin[5xπ/4] has been translated downward by 4 units.