MIDLINE

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.

Examples of Midline

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 Examples of Midline

Quick Summary

The midline is a horizontal line.
It represents the average of the maximum and minimum values of a periodic function.
It's the axis around which the function oscillates.

\[ y = \frac{max(f(x)) + min(f(x))}{2} \]

🍎 Teacher Insights

Use graphical representations to illustrate the concept of the midline. Emphasize the connection between the midline and the vertical shift of a function. Provide examples with varying amplitudes and vertical shifts.

🎓 Prerequisites

Periodic functions
Maximum and minimum values of functions
Graphing trigonometric functions

Check Your Knowledge

Q1: What is the equation of the midline of the curve y = cos(x) - 3?

x = -3 y = -3 x = 3 y = 3

Q2: The maximum value of a periodic function is 5 and the minimum value is -1. What is the equation of the midline?

y = 2 y = 3 y = 4 y = 5

Frequently Asked Questions

Q: How do I find the midline of a function?
A: Calculate the average of the maximum and minimum values of the function. This average value is the y-value of the midline.

Q: What is the equation of the midline?
A: The equation of the midline is of the form y = k, where k is the average of the maximum and minimum values of the function.