What are the amplitude, period, phase shift, and midline of fx = 2 sin(x) + 4?

The function fx = 2 sin(x) + 4 is a sinusoidal function.

• Amplitude: The amplitude is determined by the coefficient in front of the sine function. Here, it is 2. This means that the graph of the sine function oscillates 2 units above and below its midline.
• Period: The period of a sine function is calculated using the formula 2π/b, where b is the coefficient of x. In this case, the coefficient is 1 (since we have sin(x)), so the period is 2π/1 = 2π.
• Phase Shift: The phase shift is determined by any horizontal shifts in the function, defined as c/b from the general form y = a sin(bx - c) + d. There is no horizontal shift here (c = 0), so the phase shift is 0.
• Midline: The midline of a sinusoidal function is found by looking at the vertical shift, which is given by d in the general form. Here, the function has a vertical shift of +4, so the midline is y = 4.

In summary:

• Amplitude: 2
• Period: 2π
• Phase Shift: 0
• Midline: y = 4