Introduction
Today you will become what I like to call a self learner. This means that you’ll be taking learning into your own hands. This is important because as teachers we desire for you to become life-long learners.
I’m a life-long learner as well meaning I still continue to learn on a daily basis. Today you have to make the choice to want to learn. You’ll be working through a series of problems that will guide you towards the learning you need for today’s objectives.
You’ll be using your learning guide as a way to gather the information you need.
The first step is to look up the definition of inverse and add that to your learning guide. It does not have to be the mathematical definition. Try Google searching a definition and then add it to your learning guide.
Your next step is to find the mathematical definition of an inverse functions. Visit the following website for a good working definition:
Once you are on the site, try doing a search for “inverse function.” Write this definition on your learning guide. This is a great website for anytime you are struggling with a concept. They provide pictures, definitions, and practice problems. Once you finish, move onto the “Task” tab for the next step.
Task
You’ll be working to master your objectives for today. The next portion of your learning guide is your objectives. Read through them before continuing.
Once you complete an objective, mark it off your list (put a check or an x in the box). Since we have already complete objective one of defining an inverse function, mark this objective as complete. Now, move on to the “Process” tab to continue.
Process
We’ll now take a look at how to find the inverse of a function. We’ll be using the following website to walk us through the process. Visit the following website and use the information to complete your learning guide under “Process 1.”
http://www.purplemath.com/modules/invrsfcn3.htm
Once you reach the point where you begin finding the inverse by yourself, use the following links for some extra assistance.
http://www.coolmath.com/algebra/16-inverse-functions/05-how-to-find-the…
http://www.mathsisfun.com/sets/function-inverse.html
http://www.wtamu.edu/academic/anns/mps/math/mathlab/col_algebra/col_alg…
The following website is only if you have headphones:
https://www.khanacademy.org/math/algebra/algebra-functions/function_inv…
https://www.youtube.com/watch?v=q739Wcf0ZUg
Once you complete everything under Process 1, check this objective off on your learning guide under Objectives.
Process 2: (Objective 3)
Now we’ll be looking at graphing functions as well as their inverse functions. Use your learning guide and the following website to walk through graphing functions and their inverse.
http://www.regentsprep.org/regents/math/algtrig/atp8/applesson.htm
Use your learning guide to follow along.
Once you complete Process 2, check this objective off on your learning guide.
Evaluation
Today you will be graded based on the quality of your work and your effort. Yes, I can tell through your learning guide whether you have applied yourself or not! Basically, if you are a self learner today you will receive a quiz grade of 100! So, putting in the effort really pays off in the long run!
Conclusion
Now, let's sum up your learning of your objectives today! Fill out these questions on your learning guide.
Find the inverse of the following function (if it exists):
g(x) = (x+5)/2 g-1(x)=
What can you tell me about the graph of the function and its inverse?
Summarize the steps you take to find the inverse of a function.
If I am given a table of values, how do I find the inverse function (or at least its points on a graph)?
On a scale of 1-10, assess how well you have self-learned today. How well to you feel about performing the objectives? Be honest because this helps direct my future teaching.
Congrats, you've finished your learning guide and moved one step closer to being a life long learner! Once you have finished work on one of the following three options:
1.) Discussion post and responses
2.) Homework due tomorrow
3.) Literacy in math due NEXT week