This desmos project took several hours to complete, yet I am happy with the result. I did this project in grade 10, so I was familiar with the constant, linear, quadratic, cubic, square root, cube root, absolute value, exponential and rational functions. This year I learned how to graph and manipulate sin, cos, and tan graphs, as well as non-functions (relations) such as sideways parabolas and circles. When I needed to graph a new line, I would sketch the basic shape and then compared the shape to the arsenal of functions I knew, which is how I chose which equation to utilize. The main challenge I encountered was trying to shade with the relations (sideways parabolas and circles), because I am not familiar with this; however, I overcame this challenge when I rewrote the non-functions as functions (for example, when I wanted to shade a sideways parabola, I made two square root functions derived from the original equation, and then utilized them to shade the sideways parabola). Another challenge was when I realized I could not graph SpongeBob’s face with accuracy in the time I was given. So, I made a decision to modify the face so that it was easier to graph yet still held the integrity and youthfulness of SpongeBob. The aha moments of this project were when I learned how much easier it was to manipulate a basic function with function notation and transformations rather than making a new equation/function for each line, which I did in grade 10. I completed this project alone, with no help, but I did assist others. Some people were making new equations for each line rather than transforming one function over and over, and so I showed them how to transform their equations to be transformations of the same function. I told them to make a folder with all of their basic functions, and then refer to those functions when they wanted to make a new one. The main strategy I used was to make the outline of the image with functions and transformations before beginning to shade. This was beneficial, because when if I wanted to change the shape of something, I would not have to change all of the shading as well. This strategy was efficient, and I was able to complete the shading with ease. This assignment helped me understand more about transformations of functions and relations, because I spent so much time manipulating and transforming them. I was able to witness how changing the domain, range, vertical/horizontal stretch, vertical/horizontal translation could have such a drastic impact on the shape of the line.
Link to my desmos project: https://student.desmos.com/activitybuilder/instance/63b47d10b9d7d3fd3f789875/student/63c3ab49e647cadd6bde721d#screenId=6fe1849c-43b9-4a5d-b03b-31bc3cfd24d8
Original photo
My desmos project
