Lesson 8
Rising and Falling
Lesson Narrative
This lesson marks the beginning of a transition for students and their thinking about periodic functions. Previously, students approached the idea of periodic functions in the context of circular motion, such as the motion of the end of a minute hand on a clock. In this lesson, we expand the idea of a periodic function to include any function in which the output values repeat at regular intervals and show that the graphs of these types of functions can have a wavelike appearance.
During this lesson, students have the opportunity to communicate their observations about graphs precisely with others (MP6). In addition, they observe repeated behavior in graphs by contrasting them with graphs that do not repeat, which has been the norm for graphs up until this unit.
Learning Goals
Teacher Facing
 Compare and contrast (in writing) the features of the cosine, sine, and tangent functions.
Student Facing
Let’s study graphs that repeat.
Required Materials
Learning Targets
Student Facing
 I understand that the graph of a periodic function can look like a wave whose outputs repeat between the same maximum and minimum values.
CCSS Standards
Glossary Entries

periodic function
A function whose values repeat at regular intervals. If \(f\) is a periodic function then there is a number \(p\), called the period, so that \(f(x + p) = f(x)\) for all inputs \(x\).
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