Category: Grade 12

Desmos Link:  https://www.desmos.com/calculator/pbn9unkx08

Questions:

How did you figure out what equations to use?

The whole project was mainly trial and error, I did not have much experience with demos in general, so it made it quite hard to learn how to start the image. I first started by laying out all the folders for the equations and one by one going through them to figure out which function best suited the specific line I was working on. They all transform in different ways and it was some equations like rational, radical, and especially absolute values. These functions were very unique looking and only fit into the picture because I would spend half an hour just changing their shape and playing around with them until they finally matched the line. As a whole, however, I just looked at what the equation’s general function looked like, then I would look to see what lines could possibly match with it.

 

Did you have any challenges?

One of the most challenging parts of the project was honestly the colouring. Not all of the lines were using “x” as a function, a good chunk of the lines were using “y”. When colouring, you cannot use x and y equations in the same function, which made it pretty difficult when you are trying to colour in between two curved lines but they are each used with a different variable. The most annoying example of this scenario is Umbreon’s paws. I used at least 30 different equations for all of his paw lines, and even more equations when colouring them. Since I could not connect the x and y lines together when colouring, I had to keep overlapping small blobs of colour each with their own restrictions. It took forever, but in the end, I think it looks nice and resembles the original picture well.

 

Any aha moments?

This picture had a lot of weirdly shaped, intricate waves and curves. A lot of the curves would be filled in with trigonometric, logarithmic, and exponential functions. On some occasions, however, I had to be more creative. Other than using a bunch of small lines to make up one big specific wave, which takes way too long, you could also use a parabola function and then add another “x” when transforming it. This makes it a tangent graph with three x-intercepts, and because it has more points, it is more maneuverable in terms of what exactly you want the line to look like. Sure, it is probably a more frustrating method, and it is not a fast and easy approach, but it made my lines look the best that they could.

 

Did you get help?

I think it is almost impossible to not get help at least once during this project, either from a friend, teacher, or the internet. There are so many little tricky components, like overlapping different colours and having one colour be over top of another, tilting ellipses, or the fact that you can’t use y-axis restrictions on an “x” function and vice versa. There are a lot of confusing aspects about graphing and I definitely could not have finished it without bombarding people around me with questions and seeing how they did theirs.

 

Did you use any strategies?

As I have stated before, my main strategy was trial and error. I just looked at the lines I needed to fill in, saw at the different equations I could use, and chose the best-fitting one. I have been working consistently on this project since the first day of winter break, making little adjustments every day to make sure it was perfect. I saw a lot of other people’s images and noticed that some people were doing the lines and colouring at the same time, for example, doing the outline of the head, then colouring the head, and then moving on to another part of the body. For me, I did the entire outline first, so that I had the basic mould of it done, and then moved on to the colouring after. I don’t know which method is faster or more efficient, but both seem to work fine.

 

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

I already had a pretty good understanding when it came to transformations of functions since we had a full unit on it, but this project really helped me solidify that knowledge. The image I had to replicate was basically all curves and waves, which meant I had to really lean more on functions like exponential, trigonometric, and polynomials, to get it to look as close to the picture as possible. A lot of the project was repeating the same thing over and over but with a lot of bumps in the road. All of the functions I used had to be compressed, expanded, and translated all in different ways. Ellipses were good for eyes, parabolas were good for loose curves, and logarithmic was good for tight curves, all of these equations served a different purpose and I had to use all of them creatively to get the final product that I wanted. In the end, I think this assignment really helped jog my memory of what each function does and how all the different transformations can be applied to get the result that you seek.