# 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 wave-like 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.

### 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.

Building Towards

### 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 $$x$$.