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What is the midline equation of the function

h(x)=-3cos(pi x+2)-6?

What is the midline equation of the function\newlineh(x)=3cos(πx+2)6? h(x)=-3 \cos (\pi x+2)-6 ?

Full solution

Q. What is the midline equation of the function\newlineh(x)=3cos(πx+2)6? h(x)=-3 \cos (\pi x+2)-6 ?
  1. Definition of Midline: The midline of a cosine function is the horizontal line that represents the average value of the function, or the vertical shift from the standard position of the cosine function.
  2. Identifying Vertical Shift: To find the midline, we look at the vertical shift of the function. The general form of a cosine function with a vertical shift is Acos(Bx+C)+DA\cos(Bx + C) + D, where DD represents the vertical shift.
  3. Vertical Shift Calculation: In the given function h(x)=3cos(πx+2)6h(x) = -3\cos(\pi x + 2) - 6, the vertical shift is represented by the 6-6 at the end of the function.
  4. Equation of Midline: Therefore, the equation of the midline is simply y=6y = -6, which is a horizontal line at the value of the vertical shift.

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