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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 g(x)=−6sin⁡(3πx+4)−2 g(x)=-6\sin(3\pi x+4)-2 ? y=□ y=\square

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Full solution

Q. What is the midline equation of the function g(x)=−6sin⁡(3πx+4)−2 g(x)=-6\sin(3\pi x+4)-2 ? y=□ y=\square
  1. Identify Midline: The midline of a trigonometric function like g(x)=−6sin⁡(3πx+4)−2 g(x) = -6\sin(3\pi x + 4) - 2 is the horizontal line that represents the average value of the function over one period. It is the value that the function oscillates around. To find the midline, we look at the vertical shift of the function, which is given by the constant term at the end of the function.
  2. Determine Constant Term: In the given function g(x)=−6sin⁡(3πx+4)−2 g(x) = -6\sin(3\pi x + 4) - 2 , the constant term is −2-2. This means that the midline is the horizontal line y=−2 y = -2 .

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