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Unit A Concepts 8-10: Piecewise Functions, Domain, and the Difference Quotient!

Unit A Concepts 8-10: Piecewise Functions, Domain, and the Difference Quotient!

Author: Crystal Kirch
Description:

 

Evaluating piecewise functions
 
Finding the domain of a function (rational, even/odd radical, polynomials) in
interval notation
 
Evaluating the difference quotient (linear and quadratic)
(more)
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Tutorial

IMPORTANT INFORMATION...

So far, Unit A should have been very much review... at least we hope it has been!  We hope you have felt like "this is easy!"

Concepts 8-10 explore some aspects of math that you should have been exposed to in the past, but are actually relatively new.  

 

Don't expect to breeze through this tutorial, and expect that it will be a little tough.  Send questions my way so I can clarify for you!!

Please take this lesson SLOWLY, and make sure to PAUSE, REWIND, AND REWATCH the video as needed in order to ensure your understanding.

 

Congratulations, you are almost done with Unit A!

Unit A Concept 8 - Part 1

This video will introduce you to piecewise functions and teach you how to evaluate piecewise functions. It looks tricky at first, but basically you just have to identify WHICH piece the x-value fits in, and then plug it into that ONE PIECE. Just like we're used to :)

Source: Created by Crystal Kirch using Camtasia for Mac

Unit A Concept 9 - INTRO

This VERY IMPORTANT VIDEO will teach you how to write in INTERVAL NOTATION - a skill you must have mastered for this entire school year! Pay attention carefully and make sure to ask any questions below!

Source: Created by Crystal Kirch using Camtasia for Mac

Unit A Concept 9 - Part 1

This video will help us find the domain of four types of functions (helped with the acronym PREO) and write that domain in interval notation.

Source: Created by Crystal Kirch using Camtasia for Mac

The Difference Quotient Song (Winter Wonderland)

This quick song will help you to memorize the difference quotient, a formula we will be using all year and will form the foundations of Calculus next year. The sooner you master it, the better!

Source: video created by Crystal Kirch using Camtasia for Mac. Featuring 2011-2012 Math Analysis Honors students.

Unit A Concept 10 - Part 1

This video will introduce the difference quotient to you and work through an example of a linear function.

Source: Created by Crystal Kirch using Camtasia for Mac

Unit A Concept 10 - Part 2

This continuation of the difference quotient will work out two quadratic examples for you.

Source: Created by Crystal Kirch using Camtasia for Mac

Unit A Concept 10 - Part 3

This last difference quotient tutorial will go over how to find the difference quotient of a rational function.

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 9 #1-4, 6-9

Page 10 #1-12

Page 11 #1-9 (10-21 optional but suggested)

Page 12-15 #3,4,6,8

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 8 #1,2

PQ 9 #1-8

PQ10 #1-6

Unit A Reflection (Concepts 8-10)

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