When I was designing my face in Desmos, I picked functions that I thought would work best for each feature while keeping things simple, yet ensuring it is recognizably me. For the face shape, I used ellipses and parabolas to get a nice round look that was easy to tweak and keep symmetrical. The eyes are circles because they naturally have that shape, and I added smaller circles for the pupils and highlights to make them look more realistic. For the nose, I went with a mix of absolute value functions and parabolas since they gave it a clean but soft shape. For the lips, I used a combination of quadratic and sinusoidal curves to give them a natural curve and some personality. When it came to the bangs and hair, I used sine waves and parabolas to make them look like flowing strands, which made the face feel more complete. I also added a heart beside my face because it seemed like a fun and cute touch. Overall, I picked these functions because they worked well visually and were easy to adjust when I needed to.