## 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.

## Desmos Bonus Pre-Calc12 Reflection

 Completing this Desmos bonus question reflects my growth in the critical thinking competency. I spent an extra amount of time trying to figure out this question. This task required me to combine and use multiple tools that I have learned in Pre-Calc 12 in order to slowly find my way to the correct strategy needed to solve the equation. I demonstrated my resilience through this project by continuing to work on the question after multiple failed strategies; however, after each strategy, I analyzed what went right and what went wrong with what I was doing and remembered that when looking for my next attempt at solving the question. Through all of my attempts I figured out that the only way to include all of the asymptotes was to start with the backbones of the equation that would form those asymptotes. I guessed that I was on the right track once I could get each dot included but only one at a time. I had to go back and reflect on the previous lessons in Pre-Calc 12 in order to remember that the remainder of an expression where the denominator had a degree of two could have two variables therefor a system of equations for two of the dots could be found. Once I got two of the dots at a time a new I had to do the same thing but with three variables in the system of equations which led me to square one of the factors of the denominator so that I could make a system of equations with three variables. A system of equations with three variables allowed me to include all of the points with all of the asymptotes.