Link to Desmos Page: https://www.desmos.com/calculator/lw40weghjm

In this Desmos project, we were tasked to re-create an image using equations of functions and relations. We needed to include at least 1 of 10 different functions or relations in our picture. When figuring out what equations to use it would depend on the line I was looking to re-create. If the line was curved I would use a function that provided me with a curved line. However, I changed the type of function I would use for each curve. For example, I wouldn’t always use a sideways parabola, I would also use parabolas, logarithmic, exponentials, etc. If the line was straight I would use a function that provided me with a straight line. Like the curve lines, I wouldn’t always use the same function for every straight line. Instead of using linear lines every time, I would also incorporate absolute value functions with the domain and range restricted to add variety. When completing this project I ran into two major challenges. The first challenge was that when I would zoom out, completed shading would disappear as the desmos program couldn’t render all the shading. This is seen in my image above. For example, the glove looks incomplete, however, when you zoom in you can see it has all been shaded. This challenge leads to frustration as through all the hours spent on this project it looks incomplete when it’s finished. The second major challenge was shading in between sideways parabolas and other functions. Each function and relation was labeled something of x (ex, g1(x)), however, sideways parabolas were labeled with something of y (ex, f4(y)). When creating inequalities to shade between, I was unable to shade between them due to these labels. This caused me to need to go back and insert extra constant lines. Once these constant lines were inserted I was able to shade. The one aha moment I had when completing this project was when I learned that I can shade the inside or outside of an ellipse and restrict it to a function, rather than an x or y value. For example, instead of restricting the ellipse shading to (5.97>x>4.77), I was able to restrict it to (x>g18(x)). This aha moment saved a lot of time when shading around ellipses. Through the project, I got help from youtube, classmates, and my teacher. From watching youtube videos I found out how to create colors and find the correct RGB combinations of color shades. I had help from classmates on how to shade between functions using inequalities. I learned from my teacher how to correctly write in function notation. To complete the picture I used a few different strategies. First I looked at the picture and created folders about the different parts of the body I would be re-creating. I then put functions and relations next to the folder name to make sure that I used all 10. I then created my 10 base functions and relations that I would be transforming. I completed the outline of my player first and shaded him second. One main strategy I used was copying similar angled absolute value functions and using them again at another point on my player. For example, when creating the logo if I inserted a line, and later in the logo, there was a similar angle, I would take that transformed function and change the domain and range so it would fit in the new spot. This assignment helped me understand many things about transformations of functions and relations. However, there were two main things the assignment helped me to better understand. First was better understanding and visualizing the effects of adding negatives to the x and y values of functions. The second was gaining a better understanding of the effects of compression and expansion transformations on exponential and logarithmic functions.