How did you figure out what equations to use?
Before I started, I searched up each equation on google to get a visual representation of the graphs which helped me figure out which graphs would work where. I also made a copy of each equation in desmos and played around with the values to see which ways I could transform it and how far I could change it. For example, Gumball’s legs are made out of transformed exponential functions because I found out I can make them almost straight with a curve at the bottom with enough transformations.
Did you have any challenges?
One of my biggest problems was curves that seemed to be on angles. I had to get creative with the functions and the transformations I used to get the lines to fit the reference picture. Another challenge was colouring in the beginning. There were a couple of spots where I had to use weird techniques to fill the colour correctly because of the nature of the functions I used. For example, the noses of Gumball and Anais use the max function to fill it in because I couldn’t figure out a way to fill it in with inequalities.
Any aha moments?
One of my biggest aha moments was when I finally figured out how to colour efficiently. Learning about the domain and range and figuring out that I can restrict the values as well made colouring fun. It was the most enjoyable part of the process in my opinion. I loved seeing my lines get filled in. For example, there was a space I had to fill in so I made a range between the two lines, but the colour went past the spot I needed so I tried putting a restriction on one of the values and it worked.
Did you get help?
One of the first people I asked for help was one of my friends who had already done this project. I asked them about the basics of colouring and how to rotate functions. Although in the end, I didn’t rotate any functions in my final project, it was good information to have. Another amazing source of information was Youtube. I watched a video on colouring which taught me the max and piecewise equations. I used the techniques in that video in multiple areas, most notably the noses, half of the eyes, and Gumball’s head.
Did you use any strategies?
I didn’t have many strategies that I used. Most of the time I simply translated the equation into the approximate spot then played around with the values until it fit the spot, adding or changing equations if it wasn’t working. I did however move around from area to area on the image to keep things fresh in my brain. I jumped around the three characters whenever I got bored of one which helped me stay focused and allowed me to work on the project for a longer period of time.
How did this help you understand transformations of functions and relations?
It helped me understand more what the certain numbers in an equation mean for the graph. After a couple of hours working on the picture, I began getting faster because I started to know instinctively what numbers to put where to make it fit the line. It also helped me understand how the graph of one equation can work together with the graph of another. Overall it made me faster at identifying and employing transformations and helped me understand what one graph means in relation to another.