Final answer:
The transformation not performed on the function y=-2sin(3x + 1/3) is a horizontal shift or a vertical translation, as neither a constant outside the sine function nor a constant added to the entire function is present.
Step-by-step explanation:
The transformation question is asking which operations were not applied to the function y=-2sin(3x + 1/3). In this context, transformations refer to changes made to the basic sine function to create a new function. The given function is altered from the basic sin(x) function by a reflection, a vertical stretch, and a phase shift, but it does not mention a horizontal shift or a vertical translation.
By analyzing the components, we can identify the following transformations:
- The coefficient -2 indicates a vertical stretch by a factor of 2 and a reflection across the x-axis.
- The factor 3 before the x inside the sine function denotes a horizontal compression by a factor of 1/3.
- The constant added inside the sine function, 1/3, accounts for a phase shift, but its presence means there is indeed some phase shift.
Therefore, the transformation not performed on the given function is a horizontal shift defined by a constant added or subtracted outside the sine function or a vertical translation, which would be indicated by a constant added or subtracted to the entire function.