Algebra II: Functions and Inverses

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.