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