How did you figure out which equations to use?

At the beginning we were all given a list with different equations such as the linear, quadratic, cubic, square root, circle and reciprocal function. They each had their own shape and I chose the specific equation depending on which body part it best corresponds with. For example, I used the circle equation for the inside of my eye and the top of my head. The majority of my self portrait uses the quadratic equation/parabola for the eye shape, ears, nose, eye lashes face and mouth. I also used the square roots function for half of my eyebrows and the sin function rotated vertically for my wavy-ish hair. The vertical part of my eyebrows is the y=x equation. Finally I used the reciprocal function for my neck because it mirrored one side of my neck to the other. Overall my decision of which equation to use was based on what shape it made and how you could alter it to rotate it, or flip it in another quadrant. The equations that were more circular where used for the base body parts and the squiggly lines where used mostly for hair.

Did you have any challenges? Did you have any “aha” moments?

I faced quite a bit of challenges during this assignment. My biggest one was flipping one object to another quadrant. By the middle of my project I figured out that you needed to change the negatives and positives in the equation but I wasn’t sure which ones exactly. My other challenge was adjusting the positions of all the functions and relations. Creating the hair was the hardest part because I couldn’t figure out how to make the sin function vertical, therefore it would no longer be a function. In general the whole process of creating the eyes, face, eye brows and hair was very challenging. Some of my “aha” moments was when I realized that when I changed x to -x in the equation for the eyelashes, it mirrored it over to the other side. It saved me a lot of time and therefore made it quite efficient. Another “aha” moment was when I tried making my mouth with the quadratic equation and I accidentally made it too low. Before I had a oval for my head but I didn’t like how rounded my chin was and after placing my mouth too low, I created my chin from a parabola.

Did you get help? Did you use any strategies?

We had time to work on this assignment in class, so the first 10-15 minutes we bounced ideas off of each other to get started. The beginning was the hardest because you were just getting all the equations memorized and didn’t know what would happen if you changes the value or made it negative instead of positive. Since the majority of my self portrait was done at home, I would say that I experimented and testes out more strategies on my own. Some strategies that I used were seeing how the proportions changed by increasing or decreasing the coefficient and also estimating the coordinates of the x and y values so that I could get an idea before I made the equation. These strategies helped me make my self portrait detailed and accurate.

What did this assignment help you understand about functions, relations and their graphs?

This assignment taught me how the slightest difference in the coefficient can drastically change the position of the function or relation. The assignment also taught me how to manipulate the relations and functions to my advantage so that at the end I could create a piece of artwork. Functions and relations can get messy to the point that you have experimented with an equation so much that you forgot what is started as, but once you learn all the tricks they can be resourceful and also a lot of fun!

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