In this activity, the goal was to create a Santa face using relations and functions in Desmos, along with different colours and using the Domain and Range tricks we learned in class.

The first relation I used was + = 16. I knew that when you added two things to the power of two, it would end up being a circle because multiplying two negative or two positive numbers results in the same solution. Example: -4 x -4= 16 and 4 x 4= 16.Therefore for every x, there will be more than one y. I knew I wanted a circle big enough for other things to fit in.

I used my knowledge of parabolas and how they are made to make Santa his legendary beard. I said that Y had to be less than or equal to zero, so that the beard did not extend past his face. The function I used was – 15 because I wanted his beard to hit its vertex at -15 on the y-intercept.

I simply entered in coordinates for his eyes, making sure they were even spaced by using the y-axis as a middle point. the coordinates were (-1,1) and (1,1).

For his smile, I figured out which way I wanted the slant to go, and entered in my X accordingly, slanting to the right is positive and slanting to the left is negative. I eventually realized that I needed to subtract three so my y-intercept could be -3. I used the restrictions that y had to be less than or equal to zero but more than or equal to -3 so my smile wouldn’t extend too long.

Finally I created my hat. For the bottom line, I said x=4 but could only be -4 through to 4. For the two lines that reach a point, I established my y-intercept, so in this case +12, and created my slant, which was 2x. I did the same thing for the direction of my slant as in the smile. However, my restrictions were different for each. 

In conclusion, I really enjoyed this activity and working with Desmos. I look forward to more challenges like this and using Desmos in future for my graphing needs.