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What is the midline equation of the function {:[g(x)=-6sin(3pi x+4)-2?],[y=]:}

What is the midline equation of the function\newlineg(x)=−6sin⁡(3πx+4)−2?y=□ \begin{array}{l} g(x)=-6 \sin (3 \pi x+4)-2 ? \\ y=\square \end{array}

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Q. What is the midline equation of the function\newlineg(x)=−6sin⁡(3πx+4)−2?y=□ \begin{array}{l} g(x)=-6 \sin (3 \pi x+4)-2 ? \\ y=\square \end{array}
  1. Definition of Midline: The midline of a sinusoidal function like g(x)=−6sin⁡(3πx+4)−2g(x) = -6\sin(3\pi x + 4) - 2 is the horizontal line that passes through the vertical center of the sinusoid. It is the average of the maximum and minimum values of the function. Since the sinusoid is shifted vertically by −2-2, this will affect the midline.
  2. Vertical Shift Analysis: To find the midline, we look at the vertical shift of the sinusoidal function. The general form of a sinusoidal function is y=Asin⁡(Bx+C)+Dy = A\sin(Bx + C) + D, where DD represents the vertical shift. In our function g(x)=−6sin⁡(3πx+4)−2g(x) = -6\sin(3\pi x + 4) - 2, the vertical shift DD is −2-2.
  3. Midline Equation: Therefore, the midline equation is simply the constant term that represents the vertical shift, which is y=−2y = -2.

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