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What is the midline equation of the function {:[g(x)=-sin(8x-3)+5?],[y=]:}

What is the midline equation of the function\newlineg(x)=−sin⁡(8x−3)+5?y=□ \begin{array}{l} g(x)=-\sin (8 x-3)+5 ? \\ y=\square \end{array}

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Q. What is the midline equation of the function\newlineg(x)=−sin⁡(8x−3)+5?y=□ \begin{array}{l} g(x)=-\sin (8 x-3)+5 ? \\ y=\square \end{array}
  1. Identifying the Vertical Shift: The midline of a trigonometric function like g(x)=−sin⁡(8x−3)+5g(x) = -\sin(8x-3) + 5 is the horizontal line that represents the average value of the maximum and minimum values of the function. To find the midline, we need to identify the vertical shift of the function.
  2. Analyzing the Function: The function g(x)=−sin⁡(8x−3)+5g(x) = -\sin(8x-3) + 5 is a sine function that has been reflected over the x-axis (due to the negative sign), shifted horizontally (due to the −3-3 inside the argument of the sine function), and shifted vertically (due to the +5+5 outside the sine function). The vertical shift, which is +5+5, tells us the midline's y-value because it is the constant term added to the sine function.
  3. Determining the Midline Equation: The midline equation is therefore a horizontal line at the y-value of the vertical shift. Since the vertical shift is +5+5, the midline equation is y=5y = 5.

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