Link to Desmos: Holiday Card

This Desmos project has given me an opportunity to put everything I have learnt about graphing in Pre-Calc 12 into practice and to experience the fun in graphing.

I started by sketching the card onto a piece of paper. Then, I decided to draw the origin at the neck of the person with the y-axis running down the middle of the person because that is the most detailed part to graph. With this position of the origin, it’s easy for me to adjust the transformations of the functions to fit my design. After having the xy-plane, I had an overall idea of the arrangement and started graphing.

The first thing I graphed was the face, which went through the origin. Next, I moved on to the hairs and hat, and worked on to the lower body. Letters were the last thing I worked on because they were relatively basic and easier.

The functions were first chosen based on the shape of the line. Stretches and reflections were added to the original functions, together with translation until they fitted into their places; restriction was added in the end. At first, I found it time-consuming to do the transformation so that the lines are connected, as well as to reach the right size and angles. However, I gradually got used to the amount of shifting the numbers affected the functions, and I was able to work faster.

I think having a draft before graphing saves me a lot of time finding a balance for the pictures I graphed. Furthermore, having the origin, the x-axis, and the y-axis at the hardest part enables me to utilise reflections and minimal translation.