 In this short video, I will explain how to create a dataset for this particular melody and then how to create a function that represents that dataset in GeoGebra. So if we go over to GeoGebra, when you first open GeoGebra, it looks like this. I'm going to make the font size a little bit bigger so you can see it better. And then I'm going to go to View and add a window, which is the spreadsheet window. So if you see I have a window over here where I can type in data points. If I go back to the melody, the data that represents this melody based on our mathematical representation is this dataset. The first point is 0, 0 that represents kind of half of this half note and then 1, 0. So these two points together represent this note, 2, 2 represents this note, 3, 3 represents this note, etc. So I'd like to type this as a dataset into the GeoGebra file. So I'll go back to GeoGebra and in the A column I'll type in all the X coordinates. And then in the B column I'll type in all the Y coordinates. And then I'll highlight the list of coordinates and I'll right click and choose Create List of Points. If you look over here to the left, you can see that GeoGebra has created a list of points. It names them A, B, C, etc. through I. And then it also has created this list and named it, called it List 1. That will be important for us later. If you click on the graphing screen, you'll see these icons show up at the top. If you click on this far right one, you can hover over the graph until you see the panning hand and you can move it around. You can also hover over the axes until you see these double arrows and you can stretch the axes out to get a good viewing window. If you like you can change how big they are, the color of the points, those are options too. But what I'd like to do is I'd like to ask GeoGebra to fit a polynomial through this set of points. And I'm going to call that polynomial F of X. On the bottom here, on the input window, I'm going to type F of X equals. And the command for fitting a polynomial is FitPoly. So if I start typing fit, it comes up with possibilities. And the one I want is FitPoly. So I click on that one. The first parameter is the list of points. And as you can see it's highlighted in blue at the bottom of the screen. I'm just going to type in list one, tab over. And when it's all blue like that, whatever I type in will type over what it's got in those angle brackets. And then I'm going to ask for a fifth degree polynomial for example. And then if you hit enter, it creates the fifth degree polynomial using regression for this particular data set. If you don't like that particular polynomial, if you think you want to try a fourth degree or a third degree, you can change it. You can either double click up here where it says function FitPoly and change the command in this dialog box. I'm going to backspace over the five and change that to a four and say okay. And now this is the fourth degree polynomial. So you can decide which polynomial you think kind of represents the data set the best for our activity. The other thing that you can do is to define a function on a limited domain. For us this is going to be only part of our functional representation of our melody. So we only want to define it on the interval from zero to seven inclusive. So what I'm going to do is define a new function. Let's call it g of x. And I'm typing down here in the bottom, the input window I can say equals. And the command for a piecewise function is to use the command if. So if I start typing if, I can put a left hand closed bracket. And I can say zero is less than or equal to x is less than or equal to seven. And then I can put a comma. And I want g of x to be f of x for this interval. And if you'll notice it created a new function on the left hand side. It's called g of x. It's highlighted in orange here. And it's on top of this green graph which was the entire f of x. So if you want to go back and change f of x and say for example you'd rather have the fifth degree polynomial. You only have to change it here because g is defined in terms of f. And it will update both of the functions. If you'll notice the g of x is this piecewise defined function. But it actually shows you what that function is. And you'll notice that the first coefficient looks like it's a zero. If you change the rounding under options you can see more decimal places. Say for example five then you can see that those coefficients really aren't zero. If you want to see the entire function you can hover over the vertical bar on that algebra window and move out and see the function and its coefficients for each of the terms more specifically. If you want to turn off the green function now that is the entire function you can just click on this button on the far left hand side and it only shows you the orange one. If you want to change the trace type on the orange one so that it's thicker you can right click and go under object properties. And then under style you can change the thickness. You can also change those options for the list of points. I can right click on list one, go to object properties, make those bigger. I can change the color to say blue. Oh that only changes the actual color in the listing. Let's change it here under the entire list of points and make them bigger. You can see behind this box that it's making the points bigger. So this should be helpful when the students are creating their functions for their mathematical representation of their melody.