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Unit C Concepts 5-7: Inverse Functions (finding, verifying, and restricting domain)

Unit C Concepts 5-7: Inverse Functions (finding, verifying, and restricting domain)

Author: Crystal Kirch
Description:

 

Finding inverse functions algebraically

Verifying inverse functions using composition

Restricting the domain of functions to make it one-to-one

 

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Tutorial

Inverse what?

There is so much to know about inverse relationships.  Unbeknownst to you, you have been dealing with inverse relationships all along - they are anything that "undo" each other... the inverse of addition is subtraction!  The inverse of division is multiplication!  Now, we are just dealing with inverse FUNCTIONS, meaning functions that somehow undo each other?  But, how do they do that? Let's see!!!

 

 

To remind you:

Even though you may be saying, "Oh yeah, I got this"... PLEASE PLEASE PLEASE make sure to FULLY understand the details of this concept. It's MORE than just solving the problems in Math Analysis...

YOU MUST BE ABLE TO SOLVE, EXPLAIN YOUR THOUGHT PROCESSES, AND MAKE CONNECTIONS among these concepts that you have seen as "so easy" in the past.

Start yourself on the right path by taking even these "beginning concepts" seriously!

UNIT C CONCEPT 5 - INTRO

How does VANG apply to inverse functions? Watch this video to find out!

Source: Created by Crystal Kirch using Camtasia for Mac

UNIT C CONCEPT 5 - PART 1

The introduction to how to actually find inverse functions algebraically, starting with Level 1.

Source: Created by Crystal Kirch using Camtasia for Mac

UNIT C CONCEPT 5 - PART 2

More examples of finding inverse functions (level 2)!

Source: Created by Crystal Kirch using Camtasia for Mac

UNIT C CONCEPT 5 - PART 3

More examples of finding inverse functions (level 3)!

Source: Created by Crystal Kirch using Camtasia for Mac

UNIT C CONCEPT 6 - PART 1

This lesson will show you how to "verify" that two functions are inverses. This is very similar to the process of a proof, where your WORK is much more important than your answer... because your answer will always be the same! It's about the step by step work done in the right order and shown clearly that matters!

Source: Created by Crystal Kirch using Camtasia for Mac

UNIT C CONCEPT 6 - PART 2

This video will work through a few more examples of verifying inverse functions... and they are a bit trickier :)

Source: Created by Crystal Kirch using Camtasia for Mac

UNIT C CONCEPT 7 - PART 1

This video will show you how to restrict the domain of a function to make it "one-to-one". We are only going to be looking at doing this with parabolas, since it is the easiest to visualize. However, I challenge you to pick another graph that doesn't pass the Horizontal Line Test and restrict its domain after learning how with parabolas.

Source: Created by Crystal Kirch using Camtasia for Mac

SSS Requirements

 

Before moving on, please make sure the following problems from your SSS are complete and correct, as based on what I went over in the video. 

 

Page 7 #2,3,4

Page 8 #5,6,8,9

​Page 9 #1,2

Page 10 #3,4

​Page 11 - 4 problems (unnumbered)

 

Practice Quiz (PQ) requirements

 

Before moving on, please complete the following PQ problems on your own.

  • These problems must be done on lined paper and labeled clearly with “Unit ___ Concept ___ Practice Quiz” at the top of each page.  PLEASE HIGHLIGHT THIS TITLE SO IT IS VERY CLEAR WHERE ONE ASSIGNMENT STARTS AND ENDS. 
  • You must show all work, all steps, and all thought processes for these assignments.  If you feel like you don’t need to show any work, you must explain your thought process in a few sentences.  No step by step work = no credit.
  • You must check your answers to the PQ problems (answers are on the last page of each SSS packet) and re-work through any problems you got wrong.

You must MASTER this material, so if you are getting them wrong, you need to figure out how to do them correctly.  Please contact me if you have a question (you can add a question at the end of this tutorial) and I can work out another example video for you.

 

​PQ 5 #1-6

​PQ 6 #1-6

​PQ 7 #1-4

 

Unit C Reflection (Concepts 5-7)

Please answer questions posed below correctly and completely.
You MUST re-watch the video if you don't know the correct answer.

Completely means:

1) Complete sentences
2) Detailed answers

Source: Created by Google Docs