What are the Amplitude, Period, and Midline of f(x) = −7sin(4x − π) + 2?
We will be using the phase shift standard form to solve this.
Answer: The Amplitude, Period, and Midline of f(x) = −7sin(4x − π) + 2 are −7, π/2, and y = 2 respectively.
Let's solve this step by step.
Given that, f(x) = −7sin(4x − π) + 2
We have a standard form for phase shift:
f(x) = asin(bx + c) + d
Here, a = -7, b = 4, c = -π, d = 2
Where, Amplitude = a, Time Period = 2π/b, Phase Shift = c, Vertical Shift = d.
On Comparing we get: Amplitude = -7, Time Period = π/2, Phase Shift = -π, Vertical Shift = 2.
The midline is parallel to the x-axis and runs between the maximum and minimum value(i.e., amplitudes)
For the function f(x) = sinx midline is y = 0, midline is affected by any vertical shift/translations. For example, y = sin(x) + 1 has a midline of y = 1.
⇒ The midline of function f(x) = −7 sin(4x − π) + 2 is y = 2.