Link to Desmos

Out of personal interest and due to the face that Shin’s face had multiple irregularities that made perfect sections of quadratic, linear, exponential and square root functions, as well as parts of circle relations and inequalities, I decided to make Shin-chan for this assignment. Initially, I started with graphing Shin’s face. I wanted the face to be the most detailed since the face made up the majority of Shin’s body, and since the face was often where people looked at the most. I started with using quadratic functions to create parts of Shin’s face, moving the different functions through horizontally and vertically translating the functions. I experimented with linear functions, but what I found was that linear functions gave a bumpy look to his face. They worked for his eyes but marred the quality of Shin’s face when used to create his face’s outline. Through experimenting with different vertical compressions and expansions, I managed to create half of Shin’s face. Then, I decided to read the page of functions and relations for the first time and discovered circle relations. I used circle relations for corners where a function was not possible. A circle relation allowed me to have more than one output for every value of x, which was very useful for corners where I could simply use one circle relation instead of multiple functions. Also, I could use a circle relation to make Shin’s mouth in one relation. I then started using square root functions interchangeably with quadratic functions. Generally, I could use either one for the task I needed to accomplish, but when I needed a certain curve on the graph that was not achievable even when altering the vertical stretch of the quadratic function, I used square root functions. During this time, I discovered that I could square root a negative value to reflect it on the y-axis. This was an “aha” moment for me, since this wasn’t on the package and because it brought out the interesting concept of imaginary numbers. Once I had finished the outline of the face, I used inequalities, setting various restrictions on each inequality, to shade in the hair, eyes, and mouth. To make the color darker, I layered the inequalities on top of each other to create an opaque color. I then used an exponential function to create the upper part of Shin’s right hand. This area needed a line that looked linear but still had a slight curve, which made the exponential function a perfect fit. I then finished the rest of Shin using the quadratic, linear, square root, and circle relation techniques I used with his face.

I didn’t really have any challenges, but I did have questions and confusion about the process of rotating circle relations. However, as the process was too complicated, I had to find alternative methods. I asked for help from Mr. Salisbury when I had any questions and asked for input on making Shin’s eyebrows look bushy from some of my classmates. I employed strategies, such as not constantly zooming in and out, but instead translating my function so it would appear in my zoomed in screen. I also copy and pasted functions and inequalities to save time.

I walked into this project already knowing how to transform functions, relations, and their graphs, but this assignment was a useful review and helped me visualize some of the knowledge I already had, which helped clear up some ambiguity in my mind.