Yoshi and Toad Desmos Graphing Project – Alyssa Clark
(1) How did you figure out what equations to use?
For me, figuring out which equations to use was not something I found difficult. Knowing that we had to use each of the ten different functions at least once, I used that as a starting point. Once I found a place for each equation I started tracing the other lines. Sometimes I has to use many different functions to make one single line, but I just used my knowledge of the functions and shapes to find out how to trace it. Based on the functions and what they looked like graphed, I was able to try and fit them where they would work best.
(2) Did you have any challenges?
There weren’t many challenges that I faced, but one thing that I was having difficulty with was the colouring and figuring out where the best place to put the colouring functions. I was struggling with trying to get the shading above the black lines so that you could still see them. I then figured out that you have to put all the colouring functions above the line functions in order for the lines to show up on top. I was also having some struggles with the domain and range restrictions when trying to shorten the graph. There were times where the graph would disappear and reappear at random times. I then realized that I had to have the x and y restriction together instead of two separate restrictions.
(3) Any aha moments?
My biggest realization while completing this project was figuring out the function notation, being able to transform the same function while only using one equation. At first I was struggling to understand how it worked and trying to use different variables, but once I figured out how to make the general equations it was very easy to transform the rest of it. As an example I used the function notation for the absolute value function by setting a standard function of b(x)=|x| and then using a different variable, for example c and you would say c1=b and then add any transformations to the right of the b.
(4) Did you get help?
Throughout the completion of this project, I had to do a lot of trial and error with the equations and with the restrictions of the colours. Although there were times when I was struggling, I only asked for help about one thing and was able to figure out the rest on my own. I was able to watch some videos to expand my knowledge on Desoms, which helped me with the overall project. I was also able to talk with my peers about the project and discuss some strategies and the best way to make certain equations, but for the most part I didn’t get any help.
(5) Did you use any strategies?
I didn’t use a lot of strategies when completing this project, but the only thing that I think helped me was making sure I included each of the different functions first before I completed the rest of the project. I talked to a few other people who forgot to use some of the functions and had to fix some parts of their project to make it work, so I think if you make sure that you are meeting all of the criteria first it is a lot easier to complete the rest of it. I also knew that I would procrastinate while completing this project, so I made sure that I did a little bit of it each day to make sure I would have it completed in time. I took advantage of winter break and finished the outline before I cam back to school, so all I had left was the shading to complete. After the break I made sure to time out when I was going to do the shading and I was able to finish it a lot earlier than I was expecting. So making sure that I had enough time and used my time well was a very important strategy that helped me a lot.
(6) How did this assignment help you understand more about transformations of functions and relations?
I already had a solid understanding about transformations of functions and relations, but this project really helped to show and demonstrate my understanding, while also expanding my knowledge about it. Since the picture that I chose had a lot of different types of lines and circles I had to be creative and apply what I know about transformations to make the lines align with the picture. One of the functions that I used the most was the semi-circle function. In the picture that I chose there were a lot of curves, some shorter and some longer, so the transformations were essential for me to use to be able to fit the function on the line as best as possible. I had to apply vertical and horizontal expansions and compressions along with horizontal and vertical translations to shift the function. Since I had to apply a lot of transformations, it helped me to understand the concept extremely well and I wasn’t struggling to figure out how to make the function perfectly match up with the line. It also helped me to refresh my memory on all the different parts of the functions and what each one does, whether it applied to the horizontal or vertical transformation.