![]() So, I could go over all the graph’s type that I learned in Pre-Calculus 12. To make a graph I should perfectly understand the graph’s shape and characteristics because I used only some parts of the graph and I should know which part that I want. Learning about the graph and making an actual picture with the graph was a little different for me. Therefore, the second time when I was making, I was more careful, so I saved all the works in other Desmos too. When I was doing this project, I deleted all the works that I did by mistake, so I had to do it again. Also, equations are not only the problem that I faced. To put the graph in the right place was needed to make a good holiday card and for that, all the things that I learned in the Transformation unit were strongly helpful. During this project, I felt transformation was really helpful because not only the shape of the graph was important. I also got help from friends who had already done this project when I had a hard time and research on google when I want to make a specific shape with the graph such as heart. However, I found the interesting shape changes of the Sine graph and I used it not only for the hair but also for the hat. I was not sure which graph should I use to make a character’s hair looks like with my real hairstyle. Using other equations (such as exponential, radical, etc.) was a little tough but especially, hair was the hardest one for me. I made a tree and all the letters first because I thought using a linear equation was easier than other equations. I believe this assignment has come in handy especially since we have a final up and coming soon.I really enjoyed making this holiday card by using Desmos. ![]() Overall, as time-consuming as this assignment was I think it has enriched my understanding of the six functions and how to better manipulate them using translations, stretches, reflections, and domain/range restrictions. The only strategy that helped me was sketching it on paper and graphing each part of the face, tree and letters part by part to get a better understanding of the transformations of the relations. I mostly used log functions when creating the face on my holiday card. In the beginning, I asked a few friends who also turned out to be stuck, and then I went back and looked at our notes and got a clearer vision of how and where to use them. I got stuck on several occasions, especially when it came to implementing log and exponential functions. The domain and range restriction manipulation was an important factor in making sure the dimensions of the portrait and decorations do not exceed their space and intervene with other parts of the graph. What I found great about Desmos is that it pinpoints the exact point on the graph so it makes it easier for myself to set the domain and range restrictions. The rational equations helped me produce the decoration on the Christmas tree. ![]() Radical equations came in handy when I was sketching my eyebrows, I found out that their perfect curve made a good fit to add for the eyebrows. The most challenging equation to implement in my opinion was exponential, I was somewhat stuck on how to use it but ended up adding it in a form of decoration to my Christmas tree. I found the sine equations easier to manipulate than the rest. I used it to make my hairline, the letter M, R, my nose, and lips. Once I got an idea of how I wanted it to look like, I began experimenting with what kinds of equations would be easy to manipulate and which equations would be more difficult to apply. I started off with a pencil and a paper, trying to sketch what I wanted to replicate on Desmos later on. Since I am not very familiar with using Desmos besides graphing equations it took a little bit of time to get accustomed to using the website itself. ![]() I managed to underestimate how long this task this would take, not because of how difficult it was, but the fact that it was so time-consuming.
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