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Reflective Learning Journal  (Week 4)

      (The photos that I attached aren’t here)                                  

1.What have I learned this week?

 First of all, I learned about graphing. In Wikipedia, the definition of “graph” is “a diagram showing the relation between variable quantities, typically of two variables, each measured along one of a pair of axes at right angles”. Graphing is really necessary in learning functions. Next, the different types of functions which are the linear, quadratic, absolute value, constant, identity, and piecewise.

 A function is a linear function if f(x) = mx + b, where m and b are real numbers, and m and f(x) are not both equal to zero.

 Here’s an example of a linear function:

        A function is a quadratic function if f(x) = ax

² 

+ bx +c where a, b, & c are real numbers and a ≠ 0.   Here’s an example of a quadratic function:

    A function is an absolute value function if for all real numbers x,  

Here’s an example of an absolute value function:

     A linear function f is a constant function if f(x) = mx + b, where m = 0 and b is any real number. Thus, f(x) = b.

Here’s an example of a constant function:

      A linear function f is an identity function if f(x) = mx + b, where m = 1 and b = 0 Thus, f(x) = x.

Here’s an example of an identity function:

      Lastly, a piecewise function (also called as compound function) is a function defined by multiple subfunctions, where each subfunction applies to a certain interval of the main function’s domain.

Here’s an example of a piecewise function:

      Aside from the types of the functions. I also learned that An ordered pair is a pair of numbers, (x,y), written in a particular order. Also, I also learned about the mapping diagram. A mapping diagram is really helpful when it comes to distinguishing if the set of numbers is a function or not. Lastly, the table of values. Aside from the mapping diagram, this is also helpful.

Here are the examples of:

An ordered pair

                           (x, y)

                 x= first coordinate

                 y= second coordinate

  A mapping diagram

    A table of values

                                      2.      What did I think but was not able to learn in the lesson?

 I’m kind of like thinking about the piecewise function but I wasn’t really able to understand it but aside from that, just like my answer on the first reflective journal, to be honest, when I came inside the room, I can’t remember everything that is related to the lesson that we’re going to discuss because my Grade 8 teacher wasn’t able to teach us properly that’s why I’m not so familiar with everything.

 3.      What did I do and how I think/feel about this?

I listened very carefully and tried to understand everything despite the lack of information. I felt really excited to learn and also nervousness.

4.    How do I apply the topics I learned in real-life?

 I can apply these topics in real-life by comparing it to my life. It’s just like my life. It’s hard to understand but once you’ve understood everything, you’ll be able to realize many things. You will not be able to know its value when you’re not open to understand it. Understanding functions is hard, just like the meaning of life.

 5.      What question/s I need to ask in relation to the topics/lessons discussed?

 I really don’t understand the piecewise function. That’s why I have these questions in my mind like, “How to plot the piecewise function in a graph?” “What is a piecewise function?” and everything related to the piecewise function.

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Reflective Learning Journal  (Week 3)

1.            What have I learned this week?

        I learned that every function is a relation, but, not every relation is a function. I also learned how to write the domain and range in the right way. I also knew how to graph and the different types of graphs that can be used as a representation of a function. Lastly, I learned about the ways to represent a function, and how to determine if the relations are functions.

 2.            What did I think but was not able to learn in the lesson?

         To be honest, when I came inside the room, I can’t remember everything that is related to the lesson that we’re going to discuss because my Grade 8 teacher wasn’t able to teach us properly. That’s why, I have so many questions in my mind. I was really nervous because what if I will be called to answer a certain question regarding the topic? I am not familiar with the domain and range as well, I’m only familiar with the graphing.

 3.            What did I do and how I think/feel about this?

        All I did was listen. I focused listening as I became more curious about the topic since our teacher back then failed to nurture our minds. I felt really excited and quite nervous because I really am not familiar with the topic. Lastly, I felt really contented because I was able to learn the things that I wanted to learn.

 4.            How do I apply the topics I learned in real-life?

        I can apply this in time. You can’t be in two places at a time. When you try to be in two places in one time, it won’t function. You can see it when you try to graph it. Same as in a love relationship. You can’t date two persons at a time, because as a result, everything will be not understandable. It won’t function as well.

  5.            What question/s I need to ask in relation to the topics/lessons discussed.

     So far, I have a few questions in my mind. I really don’t understand the things such as “y=x^2”, when it already includes some equations. I also want to know how to connect the dots in a graph to know what type of graph it is. Lastly, I want to ask the other ways to use the functions in real life situations.