Question

what is midline of the graph? y=3 y=1 y=-3 y=0

Explanation:

Step1: Recall midline definition

The midline of a sinusoidal graph (or a periodic graph with a vertical shift) is the horizontal line that is exactly halfway between the maximum and minimum values of the function. Mathematically, if the maximum value is \( M \) and the minimum value is \( m \), the midline \( y \)-value is given by \( \frac{M + m}{2} \).

Step2: Identify max and min from graph

From the graph, we can see the maximum \( y \)-value (peak) is \( 3 \) and the minimum \( y \)-value (trough) is \( - 3 \).

Step3: Calculate midline

Using the formula for the midline: \( \frac{3+(-3)}{2}=\frac{3 - 3}{2}=\frac{0}{2} = 0 \). So the midline is \( y = 0 \).

Answer:

D. \( y = 0 \) (assuming the options are labeled as A: \( y = 3 \), B: \( y = 1 \), C: \( y=-3 \), D: \( y = 0 \))