What is the phase shift of F(x) = 3 sin (2x - 2)?

To find the phase shift of the function F(x) = 3 sin(2x - 2), we need to determine the horizontal shift of the graph of the function.

The phase shift represents the amount by which the graph of a trigonometric function has been horizontally shifted to the left or right. It is usually denoted by the variable "c" in the equation f(x) = sin(bx - c) or f(x) = cos(bx - c).

In the given function, F(x) = 3 sin(2x - 2), the coefficient inside the sine function is 2. This value, "2", represents the frequency or number of cycles within a 2π interval.

To calculate the phase shift, we need to determine the value of "x" that makes the argument 2x - 2 equal to zero. This is because when the argument equals zero, the function reaches its initial position.

Setting 2x - 2 = 0 and solving for "x", we have:
2x - 2 = 0
2x = 2
x = 1

Therefore, the phase shift of F(x) = 3 sin(2x - 2) is 1 unit to the right. This means that the graph of the function F(x) is shifted one unit to the right compared to the graph of the parent function y = sin(x).

To find the phase shift of a sine function in the form f(x) = A sin(Bx - C), where A, B, and C are constants, you can use the formula C/B.

In the given function f(x) = 3 sin(2x - 2):
- The amplitude A is 3
- The coefficient of x B is 2
- The constant C is 2

Now, use the formula for the phase shift: phase shift = C / B.

In this case, the phase shift = 2 / 2 = 1.

Therefore, the phase shift of the function F(x) = 3 sin(2x - 2) is 1 unit to the right.