In my Pre-Calculus 12 class, I was assigned a Desmos project where I had to choose a picture and recreate it using functions. I have done a similar project in Grade 10, which is why I decided to challenge myself further by creating an animated bird.

I created this project in a Desmos Classroom, so the link will not give access to everyone:
Pre-Calc 12 Desmos Project

1. How you figured out what equations to use.

I started by creating a folder containing all my functions and naming them A(x), B(x)… Since I have worked on a similar project before and I have learnt how to graph the functions given this year, I could spot parts of the picture that matched the functions. After choosing the function, I used stretches, reflections, and translations to make the functions resemble the original picture.

2. Did you have any challenges?

The main challenges I faced were understanding how to use animations using variables in desmos and recreating the curves of the bird using various functions. I also had trouble with desmos not saving and crashing due to the same variable being added to over 200 functions for the animation. I talked to my teacher, Pahlevanlu, and they thankfully created a desmos class assignment where the project was autosaved. I also created multiple variables for the animation instead of one to avoid desmos crashing.

3. Any aha moments?

I spent a great amount of time shading since I would create overlapping functions specifically for shading certain areas. When the project was almost completed, I realized that I could place domain restrictions on my shading, which would have made the process a lot easier.

4. Did you get help?

I asked Pahlevanlu for help when learning how to control all animations with a single slider and we learnt through research and smaller animations that the minimum and maximum values of all the animation can incorporate a single value, which would set all the animations off at once.

5. Did you use any strategies?

My strategy was to ensure that I used all the required functions first, to make sure I met the criteria. I then focused on small areas at a time and shaded them while creating the outline. I also made sure to have organized names for my functions (a(x) for the beak, b(x) for the eyes…) to help with the shading process.

6. How did this assignment help you understand more about transformations of functions and relations?

As I continued working on the project, I became more efficient and comfortable with graphing. This project has helped me understand the shapes and transformations of Absolute Value, Polynomial, Rational, Radical, Trigonometric, Exponential and Logarithmic, Sideways Parabolas, Semicircles, and Ellipses while creating a picture. Seeing the graphs change visually while changing its equation has been very helpful in my understanding of functions and relations.