https://www.desmos.com/calculator/eekhlgjgy5

When I was trying to figure out what equations to use for this project, I used my knowledge from previous units and the workbook to help me experiment with functions and see which ones worked best for my graph. The main challenge I came across was trying to use all 6 of the functions. When I started this project, I was mainly focused on creating the picture that I want, and I didn’t try to use all 6 functions. I just used the easiest function that would get me the picture I wanted, which was generally polynomial or semi circle functions. Once I was near to completing my portrait, I realized I hadn’t used logarithmic or exponential functions yet, so I had to go back and figure out where I could substitute those functions for one that I had used mulitple times. I also went back and created more complex functions and added more detail, to make my picture better. I worked on this project a lot before the break, because I was able to get help from my classmates and teachers in person, rather than through email, which would be my only way to get help during the break. One of my aha moments was when I figured out how to shade parts of the graph. I couldn’t figure out how to make the inequalities, and then I realized that for a lot of my functions I had just made a transformation and not named it something else. So the strategy I used to create the shading was making sure that every single function I used had a different name, even if they were transformations of a different function. This assignment helped me to understand more about transformations, functions, and relations because to be efficient, I need to memorize which functions could create which type of line, and which transformation would reflect or translate the lines in the way I wanted. By the time I was halfway done the project, I didn’t need to look at the workbook to see how To create or transform new functions, I could just do it in my head. I enjoyed this project because it was creative and a fun change from workbook questions.

By Trevor Thirsk