#### Objectives

- Students will graphically explore functions and their inverses.
- Students will find the inverse of a given function algebraically.

#### Vocabulary

- function
- inverse function
- one-to-one function
- horizontal line test

#### About the Lesson

This lesson involves grabbing and dragging point P along graphs of different functions to determine the relationship that exists between its ordered pairs and the ordered pairs of point P' that change as point P changes.

- Students will examine a set of data points. They will then examine a line and will use the ordered pairs to determine the equation of the line containing point P and the line containing point P'. They will then generate the graphs of two new lines and will write the equations of both. From this, the students will make a conjecture about how to find the inverse of a function algebraically.
- Students will examine the ordered pairs of a graph of a quadratic function and its inverse. They will be given the equation of the quadratic function in vertex form and will find the inverse of it algebraically.
- Students will algebraically find the inverses of three functions.