In this challenge, we were supposed to use Desmos and the functions/relations we learned about to create an image of Santa using domain/range, different colours and shades as well. The Santa I graphed is represented above with a full face (eyes, nose, and a smile), beard, and hat. I will explain all the ways I figured out how to graph Santa down below with a photo of the equations I used.

First off I made the base of the face, I used the basic reaction I know that creates a symmetrical circle and then used a coefficient in front of the y variable to make Santa’s face a bit more chubby since he drinks and eats so many cookies and milk! (Step 1)

From there I used the same relation to create two smaller green circle with different x and y coefficients for the eyes and their placement; this is the same method I used for the creation and placement of the nose as well and the pompom on the top of his hat, however I shaded in the pompom using an greater-than/equal-to sign. (Step 2/3/5/6)

Then I used parabolas and an upside-down parabola to create the hat and smile. For the hat I was able to use a negative coefficient, domains/ranges, and constants to flip the parabola and line it up in the perfect position with the head. Later on I created the smile while using the same technique for the hat, however I didn’t use a negative coefficient, I used positive coefficients to create the placement and how wide or narrow I wanted the smile. I still used the domain/range skills to limit where this parabola would start and end, where I used these skills in previous steps as well. (Step 4/7)

And finally I created his beard by using the absolute value function, I was able to position this function by again using a negative coefficient and then limiting where this function would go to, and that would be right to his chin by finding the x-coordinate and limiting it to there. (Step 8)

Overall, I used estimations, inequalities, coefficients, different signs, constants, and domains/ranges limitations to create this Santa graph, and don’t forget the colour, shading, and line modifications as well! In the end, this was a challenging task to complete but it taught me a lot and I taught myself a lot as well. I really enjoyed this challenge because it brought so much more knowledge to me and techniques to use for this unit.