Question

what is the equation of the midline of the sinusoidal function?
enter your answer in the box.
y = \square

Explanation:

Step1: Identify midline concept

The midline of a sinusoidal function is the horizontal line that the graph oscillates around, halfway between the maximum and minimum values.

Step2: Find max and min y - values

From the graph, the maximum y - value (peak) is 6 and the minimum y - value (trough) is 2.

Step3: Calculate midline value

The midline \(y\) - value is the average of the maximum and minimum values. So, we use the formula \(\frac{\text{max}+\text{min}}{2}\). Substituting the values, we get \(\frac{6 + 2}{2}=\frac{8}{2}=4\). So the equation of the midline is \(y = 4\).

Answer:

\(4\)