(1) How you figured out what equations to use?

I figured out most of my functions based off of the lines they made and how it would correspond with my graph. for instance, any curved lines would often be parabola’s or a formation of linear lines and or square root functions and more. For circular shapes, I often used a circle function to create that shape. Overall, If the function didn’t work out, it then came down to a process of trail and error, in order to find what functions worked best in certain scenarios.

(2) Did you have any challenges?

I had a lot of challenges throughout the project. It was difficult to accurately place each of the lines together so that it matched the image’s outline and being able to correctly use a function, that would best match the outline. It was also difficult to apply transformations in certain functions such as a circle, because it needs to be very accurate and technical, in order to make the line look presentable. I also found it difficult when coloring with certain inequalities, and being able to set domain and range restrictions for both lines and inequalities overall.

(3) Any aha moments?

In all honesty, every single time I worked on the project, there was an, “Aha” moment. Whether that may be figuring out how to effectively use a function, learning to manipulate functions or learning about coloring, each time there was also something new learned.

(4) Did you get help?

Yes, throughout the project I did receive some guidance from fellow peers or my teacher, however it was about small things, meaning that I completed this project almost completely on my own with no help, just learning things as I progressed further and further.

(5) Did you use any strategies?

Initially, I used to just make each functions as y=___, however before it was too late, I started to name my functions with variables, eg: F25(x), which helped me extremely during the long run, because setting inequalities became much easier, more efficient and less time consuming. Also, I became more aware of how to properly use and manipulate functions to my benefit, which saved me time and effort in the long run.

(6) How did this assignment help you understand more about transformations of functions and relations? 

I had no idea of how impactful and useful transformations of functions and relations are. I didn’t think that making an image would be so complex and time consuming as it was, but the end product was very interesting and looking back on it now, it’s very interesting to see how we can make such a detailed image, completely based off of the unity of equations and mathematical expressions.  

Graph on Desmos: https://www.desmos.com/calculator/j8yiq9nwau