To figure out which equations to use for my project, I would look over the functions we have learned throughout the semester and find a couple that would suit the line I am trying to graph. I would estimate how much I’d need to expand or compress to make a function more suitable for a line and test it out while altering the stretch as needed.

This was a challenging project for me. At the beginning, it was especially tricky as I didn’t know how and where to start. I was a little intimidated by all the lines I have to graph for my image and I was unsure if I was capable to finish this project. Graphing is my biggest challenge in math throughout my life, so I was really worried about this project. I hard a hard time figuring out which functions to use and how to use them. Another tricky part of this project was the shading aspect. I was really stuck on how to shade, so I watched some YouTube videos to help me. I understood most of the videos, but I had a better understanding of how to shade once I started on shading my project and experimenting with different function combinations.

I think my ‘aha!’ moment was when everything just suddenly makes sense. Around the time we were prepping for the final exam, I got the chance to properly look back on my notes and all the assignments I did. Practicing the graphs we’ve done in the past units gave me a better idea of how to start this project while using a variety of functions. I understood more of each function’s formula and what lines they would be more suitable for. After that, I was able to start working quick and diligently with a clear idea on how to work through this project.

I had some help from Christabel and Jenny during this project. I struggled with domain and range a lot since I felt that I never actually learned how to use domain and range. They taught me what domain and range can be used for and gave me examples of their own. After they gave me some tips, I was able to get the hang of it and domain and range became really useful for me during this project!

I think that most of my strategies involved trying as many functions as I could. There were many moments during this project when I would be stuck on a line and I’d have no idea which function is the best for it. when this happens, I’d properly look at all the functions we have learned and imagine them more compressed or expanded to see if there’s a function that would work best for my line. Another strategy I liked using is to check where my line will be on the graph and watch for what points are close to my line. As I graph my function, I’d scan the area to see which points are close to my line so that I’ll have a clear idea of what values I’ll need to input into my domain and range.

This assignment has helped me a lot in understanding transformations and various functions. I think that as soon as I finish a unit, I tend to quickly forget what I learned and the graphs I had done. With this project, I understood more on how to use transformations and to stretch my functions to create different types of graphs. These types of projects are very helpful as it’s a different approach to not only teach you more about transformations, but also demonstrates a different style of understanding how to use functions, rather than only work in a workbook or when preparing for a test. For me, working on a project like this helped me understand more on how to use transformations and the stretches because it doesn’t feel as restricted as homework questions on a workbook since you have to try all kinds of different functions, transformations, domain and range to create a good line.

I would grade myself a 90. I think I should’ve added more color to my image. Additionally, I’m not sure why, but there would always be spaces that’s left white despite I added shading, so I’m not sure if my shading was accurate or not. I am also unsure if my equations were creative or complex enough. I used each function at least once and I mainly focused with circle and semicircles since those functions worked well with many of the shapes in my image, such as the eyes, head, and bell.