https://www.desmos.com/calculator/9hcwdz8flr

While drawing my Pikachu, I found that the most useful functions were circles, linear equations, and quadratic equations. I mostly used those three for the body and main components of Pikachu, but I used square root and exponential functions while working on some finer details like the stripes on his back. I used linear equations to make Pikachu’s tail, including the striped detailing near the bottom. I manipulated circles to make his eyes and cheeks, and I used a combination of quadratic equations and circles for his ears. My process was very much trial-and-error, I started with a basic equation and manipulated the variables as needed. At the beginning of the project, I used variables and sliders to move my shapes, but I realized quickly that it would be more efficient to just input the numbers themselves into the equations. As I worked more on the project, I developed a method of creating the shapes that may not have been the most conventional, but was the quickest method for me. For circle equations, I wrote (y + 10)² + (x + 10)² = 10² to get a basic shape, and then estimated the proper values to substitute in for 10. This strategy helped me to visualize everything, and it made the process a lot faster for me.

My biggest challenge while doing this project was moving the equations. I was able to manipulate the size and shapes the functions with relative ease, but getting them into the correct positions on the graph was tricky. I had to really think about what I was doing to the equation to make it move. The exponential functions were the hardest to get the hang of, but once I figured out the formula, I was able to recreate it with other functions. This assignment was really helpful for my visualization of graphs and functions. I often have trouble attributing equations to lines on a graph, so this project gave me a much more in-depth understanding of what happens when you manipulate variables, or input information into a graphing calculator.