This is a Inquiry created after learning and reflecting on tools presented in  Integrating Technology in the Classroom # 6663. The following are the responses of a Sophomore in Honors Algebra 2

Discovering Inverse Functions
A Treasure Hunt on Inverse Functions

created by R. Henely
Hammonton High School

Introduction | The Questions | Internet Resources

 

Introduction

In this lesson you will use the resources of the web to learn about inverse functions. Using the different links provided you will take notes and complete various examples.

Questions

1. What are inverse functions?
   
   For all one-to-one functions, the inverse function is the set of ordered pairs obtained by swapping the ordered pairs in the original function
2. How are the x's and y's related?
   
   The x and y values are reversed
3. Is an inverse of a function always a function?
   
   No, if the graph does not pass the Horizontal Line Test, or if two or more points having the same y-coordinate, than the inverse is not a function.
4. Describe the inverse of a function graphically.
   
   The graph of an inverse function is the reflection of the original graph over the line y=x
5. How can you find the inverse of a function using algebra?
   
   Set the function equal to y, switch x and y variables, solve for y
6. Find the inverse of -4/5 x + 11.
   
   Verify if f(x) = x + 7 and g(x) = x - 7 are inverse function.
   
   y = -4/5x + 11 x = -4/4x + 11 5x = -4y + 11 y = -5/4x - 11 Yes, because f(g(x)) = x = g (f( x))
7. Determine if f and g are inverse functions.
   f(x) = 2x - 4 g(x) = .5x + 2
   
   NO, they are not invrese function Finding the inverse of f(x) = .5x + 4
8. Homework
   Pg 426 17 - 47 odd
   
   Okay

 

The Internet Resources

• Regents Math
• SOS Math
• Purple Math

 

The Big Question

Recap the basics of finding and verifying inverses.

To find the inverse, solve algebraically, graphing, of by checking f(g(x). Not every inverse is a function. Joie S Honors Algebra 2

 

Content by R. Henely, [email protected] http://www.kn.att.com/wired/fil/pages/huntinverser.html Last revised Thu Mar 22 12:03:16 US/Pacific 2007