Lecture of the Day: Piecewise Functions-Rae'ven

Blog 4: Be the Professor 

Rae'ven Hill 

Lesson for April 20th, 2015: Piecewise Defined Functions

Hello my name is Rae'ven Hill but you can call me Miss Hill or Professor Hill. Today's lecture is about piecewise defined functions.

Before I discuss the details of piecewise functions let me first define what a piecewise defined function is. A piecewise defined function is a function that employs different formulas on different parts of its domain. These functions have restrictions on which part of their corresponding graph is displayed.

Now that you know what a piecewise function is let me explain why we need to know and use them.

Math is everywhere!: Real World Examples of Piecewise Defined Functions

• A long distance calling plan charges $0.79 for calls up to 30 minutes and $0.09 for each additional part of a minute. We'd then use the cost function, C (cost in dollars and cents)= f(t-time in minutes and seconds), in terms of C(t)={79, 0 < t < 30; 79 + 9 (t-30), t > 30} 
• Buy three Kraft Instant Mac & Cheese boxes and get fourth one fifty percent off.  
  

Graphing Piecewise Defined Functions 
The second most important step of a piecewise function is graphing. I will now teach you how to graph a piecewise function.
The function is G(x)={x+1, x < 2; 1, x > 2}. Here are the four essential steps illustrated to graph this piecewise function.

In order to ensure that you fully understand how to graph piecewise functions I will explain these steps in further details. Steps 1 and 2 are just graphing the G(x)=x+1 and g(x)= 1. Step 3 involves following the restrictions for each function. G(x)=x+1 is only good when x is greater than or equal to 2 (x<2) and g(x)= 1 is only good when x is less than 2 (x>2). Step 4 then involves erasing these erasing these restrictions then adding a closed or open circle on the end of restricted line. If the restriction involves greater than or equal to or less than or equal to then it's closed circle but if it's greater than or less than then it's an open circle. So g(x)= x+1 is a closed circle because of the x<2 restriction and g(x)= 1 is a open circle because of the x>2 restriction. When you have completed all these steps, you have successfully graphed a piecewise function and you now know how to graph any piecewise function.  

   

Conclusion 
Piecewise functions are very important concepts to know as it applies to real life. Every sale in the mall or restriction on you phone bill can be graphed as a piecewise function. This lesson overall is an important concept to teach because it shows that math, even when it might not seem that way at first, can be in your everyday life.