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Unit B Concepts 4-5: Understanding, applying, and sketching shifts within parent functions

Unit B Concepts 4-5: Understanding, applying, and sketching shifts within parent functions

Author: Crystal Kirch
Understanding and applying vertical and horizontal shifts, vertical stretches and shrinks, and reflections within function notation 
Sketching parabolas, absolute value, cube root, and square root graphs with shifts
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I'm going to ruin Disneyland for you.

Sorry. But not really.  I am going to ruin Disneyland for you.  After this lesson, you will never be able to ride "It's a Small World" and enjoy it in the same way :)

Welcome to your first "real" math song of the year (you learned the difference quotient, but that was just a short formula).  It will take some getting used to, but you will soon find that learning formulas and facts to a beat is very helpful - most of us are musically inclined and can easily remember a song from the radio!  So, why not learn that way, too! 

Here are some quotes from 2011-2012 Math Analysis students about songs and chants.

  • As annoying as they got they actually helped
  • OMGGGGG! I sang them to myself like crazy during tests! :P
  • ​At the beginning the songs were weird but in the end they were helpful when i got stuck on a problem on a test.
  • Even though I don't want to admit it, the songs were usually very helpful. I still remember a lot of the formulas because of the songs. I didn't like them but they are helpful and I can see myself resorting back to them in the future
  • They are very useful and you NEVER forget them...NEVER
  • At first i thought it was pointless to memorize songs/chants but they are catchy! so when it came to the day of the test you knew the formulas due to memorizing the songs/chants. they were very helpful

So, this tutorial is all about shifting, reflecting, and stretching/shrinking functions.  We start off with a Parent Function that we will use all throughout the school year, and then learn what each of the different letters do to the graph.



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 - it's more than just rote memorization!

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

Parent Graph (It's a small world)

This song will help you memorize the parent graph formula as well as the important shifts that occur in the graph based on "a", "h", and "k".

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


This video will show you how to interpret function shifts from any given equation in "parent graph" form. We will use a tree map to organize our answers.

**Please note: In this video, I ask you to pause and actually really study and read some of the SSS on your own. You are expected to do this, because I WILL NOT be reading through it for you!!! :)

Source: Created by Crystal Kirch using Camtasia for Mac


This video will go over the details of the four types of functions we will be shifting in this unit, including the key parts, shapes, and some tricky details about root graphs!

Source: Created by Crystal Kirch using Camtasia for Mac


This video will apply everything we've talked about in this tutorial so far and actually GRAPH the shifted graph!!

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 6 #1-9

Page 7-8 #1-8

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 4 #1-8 (must do on a tree map)

​PQ 5 #1-8

(must have a tree map plus a graph with parent and shifted graph)


Unit B Reflection (Concepts 4-5)

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