What kind of reflections are the following trig functions?

y = 3cos(x-1)

y = sin(-3x+3)

y = -2sin(x)-4

To determine the type of reflection in the given trig functions, we need to examine the coefficients and signs in front of the trigonometric functions.

1. For the function y = 3cos(x-1):

- The coefficient in front of the cosine function is 3, which indicates a vertical stretch or compression of the graph.
- The expression (x - 1) inside the cosine function represents a horizontal shift to the right by 1 unit.

Since the coefficient is positive, there is no reflection in the y-axis.

2. For the function y = sin(-3x+3):

- The coefficient in front of the sine function is -3, which indicates a vertical reflection or flipping of the graph.
- The expression (-3x + 3) inside the sine function represents a horizontal compression or expansion.

Since the coefficient is negative, there is a reflection in the y-axis.

3. For the function y = -2sin(x) - 4:

- The coefficient in front of the sine function is -2, which indicates a vertical stretch or compression of the graph.
- There is no horizontal shift or reflection since there is no expression inside the sine function.

Since there is no negative sign in front of the entire function, there is no reflection in the y-axis.

Therefore, the given trig functions have the following reflections:

1. y = 3cos(x-1): No reflection in the y-axis.
2. y = sin(-3x+3): Reflection in the y-axis.
3. y = -2sin(x)-4: No reflection in the y-axis.