Desmos Art Functions Card 2020

The process I used to replicate my photo on Desmos graphing calculator was to start with the functions that would be hardest to match to the picture. Once I decided on a function to use, in order to decide where to use it, I looked for the feature that the function resembled most. A strategy that helped me to create a function that was similar to a part of the picture was to change a more awkwardly shaped function to a more useful shape, for example by creating a whole in a rational function instead of having an asymptote that makes a distorted difficult graph to use or by restricting a trigonometric function so that it takes a shape similar to a quadratic function. One of the more demanding parts of the project was the shading. Lots of accurate restrictions were needed to prevent overlap between each shading expression  and often I had to multiply the amount of expressions needed in order to shade around features I did not want covered by that colour. The eyes proved to be a problem with the shading because ellipses aren’t functions so I could not name them as one in order to define the boundaries for the shading. To get around this, I created semicircle functions to match the eyes because semicircles are nameable functions. This project was a fun way to review the functions such as ellipses and semicircles that we learned at the start of the year combined with the logarithmic and trigonometric functions that we have learnt recently. I found this project especially useful because of the way it revealed the similarities between different functions when transforming them.