Students will use an online graphing tool called Desmos to investigate the vertical transformation of the graphs of trigonometric functions as the value of D is changed in the functions:

y = sin(x) + D and y = cos(x) + D.

This will be an active learning exercise where students will discover patterns for themselves. They will have some practice problems as well. Students who discover relationships for themselves have better problem solving skills and they retain the subject matter because it is not a memorization exercise. This activity can be done in a collaborative environment as well.

Prerequisites
1. Students have learned the basics of trigonometric functions
2. Students have learned functional notation
4. Students know how to graph a function by hand given a table of values
5. Students understand the domain and range of a function.

The Activity

Students are first given a simple sine or cosine function where they add a dynamic variable (D) to the function. The graphs are either y = sin(x) + D or y=cos(x) + D. They are asked to graph the function using a free online graphing program called Desmos with the value of D being a slider. Students are also introduced to the concept of the centerline of a sinusoidal curve. They are then asked to move the slider and decide how the value of D changes the equation of the center line.

The slider feature of Desmos allows a student to dynamically change the graph of a function as they change the equation by using the slider. This helps students to discover patterns in a much shorter space of time then it would take if the students graphed each graph by hand.

Students are asked follow-up questions to test their understanding of what they have learned.

What the Student will Discover

Students’s will discover how to move a function vertically up or down by changing the value of D