For this assignment, we were told to make a graph of Santa Claus’s face using an online graphing calculator called Desmos. I used a variety of functions and relations but there were 3 main relations I took advantage of: + = n, x = , and y = . These relations made great shapes for a basic face.

I used the relation, + = n for all the circles in this graph. I would adjust n to become larger or smaller depending on what it was used for. When I wanted the center of the circle to be somewhere other than the origin, I would make brackets for the equation and add or subtract to x and y.

Both x = and y = would create parabolas which were very helpful to me when I was making the hat for Santa. I also used parabolas for the beard, in order for me to make he semi circles for the beard I had to use a parabola and restrict its domain and range to become a small semi circle. Another way I tested the beard was by making a circle then restricting its domain and range to become a semi circle.

Another relation I used during this assignment was: √x. I only used this twice, both times were used when I attached the ball to Santa’s hat. I restricted its domain and range as well as raised the y value to be the appropriate height.