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Unit B Concept 3: Graphing Piecewise Functions

Unit B Concept 3: Graphing Piecewise Functions

Author: Crystal Kirch

Graphing piecewise (2 and 3 pieces) functions

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Who owns the fence?


Welcome to the wonderful world of Piecewise Functions... that is, a function broken into pieces!  So, instead of have one equation that you graph for ALL x-values, you will have two or three (and later in the year, four or five!) different equations that are each graphed for certain x-values.  The boundaries between each graph are called "fences", and it is important to know which equation OWNS the fence and which equation is JUST RENTING it. That way we make sure that our graph still represents a FUNCTION (meaning it passes the vertical line test!)

The easiest way to start off with these fun little guys is to make an extended t-chart like you'll be shown in the videos.  However, I soon hope you find easier ways and shortcuts on how to graph these as you understand them more.


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!


This video will introduce you to how to graph piecewise graphs using an "extended" x/y table. You will learn a "trick" on how your graphing calculator "table" feature can help make this easier for you. It is important to remember that piecewise functions must remain that - FUNCTIONS - they must pass the vertical line test at all points! This means that any "fence" can only have ONE closed circle on it. TWO CLOSED CIRCLES ON A FENCE = not a function!

(HOWEVER, you can have TWO OPEN CIRCLES on a fence - that just means everyone's renting!)

Source: Created by Crystal Kirch using Camtasia for Mac


This video will review two more examples of piecewise graphs.

I made a small mistake in #1... Doesn't affect the graph but does affect the table. Can you find it? We call these "cheesebuckety mistakes" in my class :)

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.


"intro" problem from page 4

Page 4-5 #1,3,4



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 3 #1-2

Unit B Reflection (Concept 3)

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