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What is the midline equation of the function h(x)=−4cos⁡(5x−9)−7?h(x)=-4\cos(5x-9)-7? \newline y=□y = \square

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Q. What is the midline equation of the function h(x)=−4cos⁡(5x−9)−7?h(x)=-4\cos(5x-9)-7? \newline y=□y = \square
  1. Trigonometric Function Midline: The midline of a trigonometric function like h(x)=−4cos⁡(5x−9)−7h(x) = -4\cos(5x-9) - 7 is the horizontal line that represents the average value of the function over one period. It is the vertical shift of the function from the origin.
  2. Vertical Shift Analysis: To find the midline, we look at the vertical shift of the function. The vertical shift is given by the constant term that is added or subtracted from the trigonometric function. In the given function h(x)=−4cos⁡(5x−9)−7h(x) = -4\cos(5x-9) - 7, the vertical shift is −7-7.
  3. Equation of Midline: Therefore, the equation of the midline is simply y=−7y = -7, which is a horizontal line at the vertical shift of the function.

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