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What is the midline equation of the function

{:[h(x)=5sin(4x-2)-3?],[y=◻]:}

What is the midline equation of the function\newlineh(x)=5sin(4x2)3?y= \begin{array}{l} h(x)=5 \sin (4 x-2)-3 ? \\ y=\square \end{array}

Full solution

Q. What is the midline equation of the function\newlineh(x)=5sin(4x2)3?y= \begin{array}{l} h(x)=5 \sin (4 x-2)-3 ? \\ y=\square \end{array}
  1. Find Midline: The midline of a sinusoidal function like h(x)=5sin(4x2)3h(x) = 5\sin(4x-2) - 3 is the horizontal line that the function oscillates around. It is found by taking the average of the maximum and minimum values of the function. Since the function is in the form of Asin(BxC)+DA\sin(Bx - C) + D, where DD represents the vertical shift from the x-axis, the midline is simply y=Dy = D.
  2. Calculate D Value: In the given function h(x)=5sin(4x2)3h(x) = 5\sin(4x-2) - 3, the value of DD is 3-3. Therefore, the equation of the midline is y=3y = -3.

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