What is the shift along x of the following trig functions?

y = (3sinx/2) + 4

y = -2sin(x)-4

y = sin(-3x + 3)

To find the shift along the x-axis for each trigonometric function, you need to understand the concept of phase shift. The phase shift represents the horizontal translation of the graph of a trigonometric function.

1. For the function y = (3sin(x/2)) + 4:
The general form of the sine function is y = A*sin(B(x - C)) + D, where:
- A represents the amplitude,
- B represents the frequency (or how many cycles occur in a given interval),
- C represents the phase shift (the horizontal translation),
- D represents the vertical shift.

In this case, A = 3, B = 1/2, C = 0, and D = 4.
Since C = 0, there is no horizontal shift. The graph will not be shifted left or right.

2. For the function y = -2sin(x) - 4:
Similar to the previous example, A = -2, B = 1, C = 0, and D = -4.
Again, C = 0, so there is no horizontal shift. The graph will not be shifted left or right.

3. For the function y = sin(-3x + 3):
Here, A = 1, B = -3, C = 3, and D = 0.
Since C = 3, there is a horizontal shift of 3 units to the right.

Therefore, the shift along the x-axis for the given trigonometric functions is as follows:
1. No shift (left or right)
2. No shift (left or right)
3. A shift of 3 units to the right.