Question

determine the equation of the midline of the following graph.

Explanation:

Step1: Recall the formula for the mid - line of a sinusoidal function

The mid - line of a sinusoidal function \(y = A\sin(Bx - C)+D\) or \(y = A\cos(Bx - C)+D\) is given by \(y = D\). Another way to find the mid - line is to use the formula \(y=\frac{y_{\text{max}}+y_{\text{min}}}{2}\).

Step2: Identify the maximum and minimum values of the function from the graph

From the graph, the maximum value \(y_{\text{max}}=-2\) and the minimum value \(y_{\text{min}}=-4\).

Step3: Calculate the mid - line

Using the formula \(y=\frac{y_{\text{max}}+y_{\text{min}}}{2}\), we substitute \(y_{\text{max}}=-2\) and \(y_{\text{min}}=-4\) into the formula:

$$
LATEXBLOCK0
$$

Answer:

$y = - 3$