Desmos Art Functions Card 2020

For my pre-calc 10 math class, I was challenged to replicate a photo using functions and shading. At the beginning I was mainly utilizing the functions I was the most familiar with, such as the linear function, constant function, quadratic function, and exponential function. However, as I started to slowly incorporate the functions that were still fairly new to me, the square root function, absolute value function, and the cubic function, I began using them more frequently. My knowledge on these functions and how various components of an equation can manipulate the function it produces definitely developed with this project. I figured out what functions to use by analyzing my original photo and searching for where specific functions could be utilized. If I needed a slanted, straight line, I would use the linear function or absolute function. Since vertical lines are not functions, we weren’t allowed to use them, so often when my photo required a vertical line I would use the exponential function. The constant function would be used for horizontal lines. The cubic function, quadratic function, and square root function were used for any curved lines.

When working on this project, I started by replicating myself first, since I was in the centre of the photograph. Then I tackled the road, and eventually completed the houses from left to right, attempting to adjust the shading in the process to depict the brightness from the sun and how much darker the surrounding area is that the sun doesn’t reach.

There were definitely challenges along the way that I had to overcome. The shading is a significant aspect to consider when replicating a photo. There were only six colours available on Desmos, so I had to adapt and figure out how to properly overlap colours, and adjust their transparency and weight to create colours that were similar to my photo. The sun beaming down in my photo is something I really wanted to capture in my project, so I overlapped various colours and transparency levels to attempt to replicate the beautiful orange and yellow tones. Another challenge I encountered was the construction of the large tree. At first, I thought it would be easier to create an abundance of lines to form the tree rather than create an outline and shade it in. However, that was extremely difficult and unrealistic to accomplish, so I decided to challenge myself in another way and utilize square root functions instead, and so the left portion of the tree is created using square root functions as an outline.

As I was completing this assignment I had a realization; although I was tempted to utilize many small lines to achieve the perfect outline of an object or part, I learned that it is much more visually appealing when you attempt to use fewer lines since you can create this smooth, elegant shape rather than having multiple angles from trying to connect numerous little lines.

A strategy I utilized for this project was outlining a specific part or object, and then immediately shading it in after. This technique helped me tremendously since I was able to fully complete an outline and then shade the section in while still having the equations fresh in my mind, and then just entirely move on. Another strategy I used was just ordering my functions in each folder in a specific order, and this was extremely beneficial since I wouldn’t have to continuously check which functions I need to shade because I knew what order they were in.

Overall I enjoyed this project, and persistently utilizing these functions strengthened my ability to manipulate and maneuver previously learned and new functions.