Desmos Card

Figuring out what equations to use was hard. It seemed so simple to just add linear equations everywhere and move on with your day, but I really wanted a challenge and to create something unique and accurate. So, I decided to draw functions I knew out on a separate page and see what they resembled the most. I stared at a tangent function for so long until I realised I could use it to make ruffles. Creating the function first helped me notice things like how a polynomial function resembles the bend of an arm. It is hard for lines to resemble the human body, but as long as there are similarities, I think it is understood. This was very time consuming and frustrating at times, but in the end, I was able to find a spot for every function. I also found myself challenged with, not only which function to use, but how they can be transformed for the necessary spot. Domain and range had to be so precise, sometimes to 4 decimal places, in order to have the function in the right spot. Because some functions were chains of other functions, one change could affect 3 other lines, so there was a lot of work put into making sure everything was in the right place. Aside from the frustrating moments, there were also moments of excitement. It was a great feeling to figure out a perfect function for a shape that wasn’t a linear function or quadratic. I was proud to see it fit, a complicated function with the right transformation and domain and range, it was a relief. Sometimes, none of the functions fit into the idea I had. At these times, I searched on google for the equation of a circle for instance. This assignment was, in the end, a lot of fun. I liked that, when creating myself, I could add things like my nose ring. You get to learn that one f(x) can be changed and moved in so many ways. Functions are more than what you learn in class. I was able to take one f(x) and stretch it to create a wider shape or move it over to create a new shape. This gave me a better understanding of how important your stretches, reflections, and translations really are and how what a great impact they have on a function. A function that looks pretty straight can be stretched to have a wider curve or an angled slope. It also saved me a lot of time. I could make one shape and multiply it to move it somewhere else or reflect it to the other side of the graph. This was really helpful to understand in shaping my card. I am really happy with my card and enjoyed the process and the things I learned along the way.