determine the equation of the midline of the following graph.\nanswer

Answer:

$y = - 4$

Explanation:

Step1: Find the maximum and minimum values

From the graph, the maximum value (y_{max}=-3) and the minimum value (y_{min}=-5).

Step2: Calculate the mid - line

The formula for the mid - line of a sinusoidal function (y = A\sin(Bx - C)+D) (or (y = A\cos(Bx - C)+D)) is (y = D), and (D=\frac{y_{max}+y_{min}}{2}). Substitute (y_{max}=-3) and (y_{min}=-5) into the formula: (D=\frac{-3+( - 5)}{2}=\frac{-3 - 5}{2}=\frac{-8}{2}=-4). So the equation of the mid - line is (y=-4).