Algebra II: Power Function Inverses

Objectives

• For power functions of the form f(x)=xⁿ, where n is a positive integer and the domain is all real numbers, students will be able to identify which functions are invertible (odd powers) and be able to graph the inverse function using reflection symmetry across the line y = x.
• Students will be able to identify a suitable restricted domain for an even power function to have an inverse, and be able to graph the inverse function using reflection symmetry across the line y = x.

Vocabulary

• inverse
• reflection
• domain
• one to one functions
• horizontal/vertical line test

About the Lesson

This lesson involves examining the graphs of power functions with even and odd integer powers. Students will look for conditions under which the functions have inverses. As a result, students will:

• Be able to recognize graphs of inverses as reflections over the line y = x
• Be able to find points on the graph of an inverse function by exchanging the x and y coordinates for points on the original function
• Be able to state when power functions have inverses (i.e., odd power functions with domains for all real x, and even power functions with the domain restricted to values x greater than or equal to 0)