Normally, I immediately click with our math topic, and I quickly become proficient with it, but this topic was different. This topic was graphing piecewise functions. Piecewise is when you graph a line, and the line has restrictions and can continue somewhere else on the graph. A piecewise equation, can have multiple equations in it. I had trouble understanding piecewise this year, but with some studying and practice, I became and more knowledgeable  better at piecewise.

 

Something that helped me understand piecewise was a tutor session I had with my teacher during mid-day. My teacher, Dr. Schaefer, had noticed that I was struggling with piecewise graphing, so she had me come in during mid-day to practice with her. Piecewise is a way of graphing functions that involves multiple equations with restrictions (I will talk about those later). This means that the line in the graph could be in multiple spots and continue for varies lengths. It was during this meeting that I understood what the piecewise equation was asking me to do. An example of a piecewise equation is f(x) = 2x, x<5. This equation, translated into English, means f of x equals 2x, through everything less than 5. f(x) means function, by the way. In math, a function means a relationship between an input and output. This meeting with Dr. Schaefer opened up my mind to what piecewise is, but knowing me, I would eventually forget what I learned, so that night I looked more carefully at what My teacher and I had done.

               

That night at home I really paid attention to my homework. At home I looked at what I had learned during the mid-day session I had with Dr. Schaefer, and I understood it better. Whereas at school during the mid-day session I started to understand, at home I finally started to grasp what we were really doing. At home I realized that f(x) meant y, in a way. Realizing that f(x) meant y (y in mathematics represents the output of a function, or is the vertical axis) really helped me understand, as it seemed that f(x) was what was confusing me. Another thing I realize that night was what restrictions are. Restrictions (also called constraints) are limits to the x- and/or y- values. They limit the inputs and/or the outputs of a function. A line can not go through that restriction, making them segmented to that area of the graph, and since there can be multiple equations in a piecewise graphing function, that means that line will only be in that area of the graph.

               

Each of these helped me grow this year because the mid-day session helped get my head going as to what it was that I was doing, and practicing that night helped me remember it and helped me get my head around it even more. Because I practiced, I passed the class and understand piecewise graphing now. As you can see, I really did grow in piecewise this year. It took some time, but I finally did click with piecewise. If I hadn’t learned piecewise, then I would have had a more problems than just with grades. I would also have problems with my future career, as I want to become an engineer when I get older.