Some of the shading and stuff has trouble loading but it is there.
Desmos Link
Original:
Reflection
How did I choose what equations to use?
I had a sheet from early on in the year that showed the shape of the majority of the functions, so I referred to that a fair bit. Otherwise I would just plug in one of the functions that I knew I would need to use in order to meet the criteria and then manipulate the function until it matched a line that I had decided was similarly shaped. Plenty of experimentation.
What challenges did I come across?
Keeping everything organized. What a nightmare. At least I managed to develop a bit of a system with the folders to keep things from getting too cluttered. Once I separated the inequalities from the folders with the rest of the functions, it started to look a lot tidier.
I also tried to invest some time into learning how to use desmos to it’s full extent before really starting in the hopes that I might make life easier for myself in the long run. Early on, I experimented with making things like ellipses into functions of (x,y) and transforming the shapes with function notation but it was a bit of a pain in the neck and I ended up wasting a chunk of time when I was trying to save myself some of the hassle.
I also forgot to add any radical functions, so I had to replace a function with one once I had already finished.
Any aha moments?
Deciding to listen to jazz while working. My productivity immediately skyrocketed.
In a math/desmos sense, I don’t think I was struck with any game-changing progress at any point. It was just a steady learning curve for the first week or so, and then from that point forward I felt like I fully had the hang of things.
Where did I find help?
I got the most help from the internet. When it came to rotating functions, shading, custom colours, etc., google was the first place I went, and I was never disappointed by the answers I got. It also probably didn’t hurt to be sitting at the same table as a couple of people who aren’t too bad at math, as they were sometimes helpful.
What strategies did I use?
When I noticed a function’s shape could be used more than once with few transformations outside of vertical or horizontal shifts, I would just define it as a new function and slap those translations onto it to make the new functions for those repeated shapes. Saved a fair bit of time that way, and made my life somewhat easier when it came to the shading.
How did this assignment help me understand more about transformations of functions and relations?
While working on this project, I spent a fair few hours staring at functions, manipulating them to my exact desires, which means that the knowledge of how to transform functions has been deeply and involuntarily burned into my mind. I think that by actively applying the knowledge I had on the transformations of functions (in a more hands-on way), I have developed a deeper understanding on the subject, which should be expected when someone spends a lot of time practicing something.