When choosing an image I would be duplicating for the next week using solely functions and relations, I knew that the most logical decision would be cartoon characters for the simplicity of their design. I chose Sandy from Spongebob predominately because of the curves of the drawing, which I thought would be easy to replicate using circles and parabolas. However, this wasn’t the case when I recreated the drawing. I ended up using a variety of parabolas, quadratics, circles, linear equations and even an exponential function. Lines I thought would simply use circles I ended up using a multitude of parabolas and quadratics on. Before I applied any equations to the graph, I looked at my initial picture and imagined what lines would work best to replicate that shape. I used that strategy throughout the project, deviating when things didn’t look quite right and using the next probable equation to remedy the problem.
The only real struggles I faced were the transformations of the lines. I figured out early on that by making the x and y variables negative I could perform vertical and horizontal reflections of equations over the axes. Occasionally I would need to perform angular rotations or in one specific case, an overall increase in the size of a sin function, and would have no idea how to do so. To resolve this, I looked for alternative ways to carry out the task. This may have resulted in more work to achieve the same result, but I worked with what I knew. This project helped me develop and apply my knowledge of relations and functions while thinking of them more visually and less like simple numbers and letters on a page.