https://www.desmos.com/calculator/hqf7bmrhp5

My approach to this project was very much trial and error. Though I had a general idea of what I wanted to create, I had to combine multiple smaller images of a fan, some wave designs and some free-handed work to complete the design.

fan-shape-3                wave-image

Being able to superimpose an image behind my graph was incredibly helpful in the construction of my image, as turning the pictures on and off during their individual design allowed me to focus on individual, potentially overlapping lines. Usually to decide what type of graph was required, I would fill in an equation with variables and small numbers to see what the shape turned out as, and then I would situate it where it fit best on my picture. After about a class and a half, I managed to start completing transformations of graphs with little to no thought as I relaxed into the patterns. I started to develop a fairly good eye for the numbers that would be required for specific angles and intercepts. The most challenging aspect of this project was finding equations that fit some of the lines I wanted to draw. I had to scrap a couple of ideas that just couldn’t be drawn with my knowledge of functions and equations. Whenever I was lost for ideas or how to draw a certain shape I would go look at a couple of other peoples’ projects and if I saw the shape I wanted  I’d ask them how they did it to apply to mine. Overall, I am happy with my end result and I really enjoyed the project. Being able to experiment and try new techniques on Desmos helped me to develop a comprehensive understanding of transformations, while still completing a really enjoyable project. :)