Midline
Definition Of Midline
The midline is a horizontal axis that is used as the reference line about which the graph of a periodic function oscillates.
More About Midline
The equation of the midline of periodic function is the average of the maximum and minimum values of the function
Examples of Midline
Figure-1 shows y = sin x and Figure-2 shows y = sin x + 1. The second curve is the first curve shifted vertically up by one unit.
The midline of y = sin x is the x-axis and the midline of y = sin x + 1 is the line y = 1.
Video Examples: Midline, amplitude and period of a function
Solved Example on Midline
Ques: Which of the following is the equation of the midline of the curve y = cos x - 3?
Choices:
A. x = - 3
B. y = - 3
C. x = 3
D. x = 3
Correct Answer: B
Solution:
Step 1: The equation of the midline of periodic function is the average of the maximum and minimum values of the function.
Step 2: The cosine curve varies from - 1 to + 1 . So, the maximum value of the function y = cos x - 3 is - 2 and the minimum value of the function is - 4.
Step 3: Therefore the equation of the midline of the given function is the line 