Q. What is the midline equation of the functionh(x)=−3cos(πx+2)−6?
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.
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)+D, where D represents the vertical shift.
Vertical Shift Calculation: In the given function h(x)=−3cos(πx+2)−6, the vertical shift is represented by the −6 at the end of the function.
Equation of Midline: Therefore, the equation of the midline is simply y=−6, which is a horizontal line at the value of the vertical shift.
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