 In this short video, I'm going to demonstrate how to create a data set in Desmos and then how to create a polynomial regression for that data set. So this should be helpful when students are creating their math and music representation and then creating a function to represent that. So this is the data set that corresponds to these two measures of music and the math and music lesson. So I'd like to create a data set for these points and then I'm going to try to create a polynomial function that will represent this data and then we'll define that polynomial function on a subset of the real line on the interval from 0 to 7. So the first thing I want to do is go to Desmos and then click on the plus symbol up here add item and choose table and here x1 and y1 are going to represent my data set. So I'm going to type in all the x coordinates for my data set and I'm going to type in all the y coordinates for my data set and you can see over here that Desmos has created that graph of those data points. So I'm going to go here to the second slot. I'm going to type in a couple of commands, a command that will ask Desmos to create a polynomial regression for these data points. So as you can tell up here that Desmos has called these x1 and y1, I'm going to use y and then I'm going to type the number one and it automatically makes it a subscript. And then I'm going to type the tilde, which is the symbol, to ask for the regression. So this is where I might decide I want a third degree polynomial and so I need the coefficients of the third degree term, the second degree term, etc. And I'm going to use the lower case letters a, b, c, and d. So I'm going to type a x1 raised to the third power plus bx1 raised to the second power plus cx1 plus d. And Desmos has created this polynomial with these coefficients to approximate this data set. So the next thing I want to do is I want to define a function, call it f of x, and it will be the third degree polynomial with these coefficients. So it will be a x to the third plus bx to the second plus cx plus d. And then I want to define a new function g of x, which is f of x, but only defined on the interval from 0 to 7. So I'm going to define g of x is equal to f of x. And the way you limit the domain of the function is to use curly braces. I'm going to type in 0 is less than or equal to x is less than or equal to 7. Close the curly brace. And you can see that this blue function is my function f of x with a domain limited. I can turn off the f of x and the regression model, the original regression model, and you can see that this is just that function defined on the interval from 0 to 7. So if you wanted to create a polynomial regression that's of higher degree, say x to the fifth, you could do the same thing in this particular command up here. You would type in y1 tilde and then you'd use some other, you need some more letters in here, but you could say ax to the fifth plus bx to the fourth plus the x squared, etc. And then Desmos would create that model. And then the rest of this is similar in terms of how you would define a new function and then limit the domain of that function.