https://www.desmos.com/calculator/tiiaamrmv2
When I was first introduced to this project, I immediately knew it would be a challenging one. I remember when we were first taught to graph linear functions in grade 9, I couldn’t remember which direction was the X-axis and which direction was the Y-axis. Graphing used to be my least favourite unit in math because I simply just did not understand; but now observing what I have created using different types of functions and transformations, I reflect on how I have improved and come to enjoy it.
My first though that came to mind was “How am I going to incorporate a self portrait?” I knew I had to have a Christmas tree because every year my family and I decorate ours together, so I decided to start here. When I initially began my project, I created the candy-cane patterned boarder then I started with the tree. I was not happy with my first tree, I had trouble positioning it in the correct spot and positioning the linear functions to create a nice shape. Then after all of that frustration I accidentally deleted the whole thing.. Although this happened, it was beneficial because it gave me a fresh start. I was able to re-build a better tree that I was happy with. I then created the star on top using linear functions, the string decorations using sine functions, and the ornaments by overlapping different coloured circles. I created the presents under the tree by using rational functions as the ribbon around the box, and polynomial and radical functions as the bow on top. For the portrait I originally tried vertically expanding a circle for the head shape, then I decided to use the bottom of a quadratic equation as well as linear lines with various slopes to create a more realistic shape. I then used various types of functions to create the facial features which are shown in the above link, as well as dimples to show that I am smiling and happy. My most challenging unit so far in pre-calculus 12 has been the Exponents and Logs unit so I really wanted to find a way to incorporate these types of functions in an interesting way. I did so by using them to create antlers on my head, it was challenging at first to figure this out but then I began to understand. I created snowflakes because I love the snow even though it is minimal here where we live. My favourite part of my creation is the snowflakes, I was really excited when I figured out a way to make the snowflakes move in a way they look as if they are shimmering or twinkling in the background.
Overall, I really enjoyed this assignment because it challenged me and gave me an opportunity to further understand how to create different shapes using various functions and transformations. This project is unique and is a fun way to experiment and learn about different functions. It has allowed me to become aware of how much I actually understand and what I need to improve on. I am very proud of what I created for this project and I am happy that I was able to refresh my memory on functions we learned in the early semester.
