Desmos project link: https://www.desmos.com/calculator/0w5izfplxr

Please Note: When loading my demos project, demos show some parts of the colouring as blank. However, I have coloured everywhere I liked, simply zoom in to see. It must be a loading issue.

Please Note: I decided to make something original for this demos project, as mentioned briefly in the paragraph below, I have graphed the map of Iran, and graphed the northern and southern borders to replicate the outline of the Iran imperial flag. Additionally, I graphed another photo of the lion in the imperial flag.

Reference photo of the Iran map along with the northern and southern border outline:

Source: https://lizardpoint.com/geography/iran-quiz.php

Reference photo of the imperial lion emblem:

Source: https://www.pinterest.ca/pin/611504455634467461/

This Desmos Arts Function project for Pre-Calculus 12 is a midterm project that our class was assigned to do in 2022 to 2023 to draw any image of our choosing: what I chose to do was to draw the map of Iran and to make this drawing my own by drawing the flag colours in a sequence of the outlines of the northern and southern provinces, as well as showing the imperial lion emblem from the Pahlavi Dynasty flag. When drawing the outline of Iran’s map, I had to consider the heavy details of the great natural barrier (western provinces bordering Iraq), the border with the Persian Gulf, as well as the border with the Caucasus. To ensure that the map was as accurate as possible, I decided to rely on complex graphs with good use of transformations: rational functions, cubic functions, square root functions, exponential functions, semi-circle functions, and more are such graphs I decided to rely heavily on addition to the other graphs that were required in the criteria. I figured out what equations to use when I looked at a particular section of Iran or a border of the provinces. These borders are complex in shape and thus would require graphs such as a rational function to make up 3 other simple equations. When I began the project, I faced numerous challenges when considering the amount of detail that I should or should not put the effort into. I found out quickly that more attention to detail requires much more time to perfect. The great natural barrier of the map is seen to be the most detailed and I would say that it took me over 4 hours to complete. Additionally, trial and error were my enemies in this project as I was trying to find the perfect equation that had the perfect curve to it (with respect to the transformations used). Thus, my primary challenge was to decide which equation was most useful when graphing the borders of my map. One of the biggest ‘aha’ moments I had was while I created the northern and southern province outlines with the use of rational functions. As seen in my project, there were lots of grooves, ups, and downs. Thus, to make use of the rational functions, I decided to use them for this specific piece in my project. However, I discovered that I had issues transforming rational functions. It began with me not even knowing how to create the equation to transform it according to the criteria. What I later learned, and used, was that I would have to create the custom rational function, then transform it using separate functions in accordance with the specified rules of transforming. Learning this made me more efficient in the accuracy and general quality of my project. To learn this method, I had help from my peers who had similar experiences as I did. Though I did not rely on the internet guidance, I did have one-on-one discussions to figure out equations and transformations. While creating my project, I used one primary strategy to replicate my photo, but put less stress on the attention to detail that is heavily required for the specific image that I have chosen. I decided that I would simplify areas that required heavy detail and keep true to the original shape and form of the borders. Furthermore, I would use a similar equation to replicate the same curves of the map. But, again, not paying attention to every angle for as long as it looks fairly similar. Using this strategy resulted in my overall efficiency and the satisfactory replication of the Iran map. Overall, I have learned how to apply transformations to all sorts of equations and functions that vary in difficulty and complexity. This project has allowed me to understand specific transformations to create a specific image that combines other functions and equations. Furthermore, I understand the variable and value changes of inverses, stretches, and transformations, which now allows me to be more specific with my graphing.