REFLECTION:

There are many things that I've learned in this module and in this summative test that have been discussed all throughout the first quarter. First and foremost, functions. I've learned that you can easily tell whether the equation is a function or relation just by looking at the two ordered pairs given and by using the vertical line test. I actually kept this in mind that all functions are relations yet not all relations are functions. Furthermore, there are different functions that were discussed and included in the summative test and these are the rational function, one-to-one function and the inverse function. Rational function is the function in which two polynomial functions are needed to be written in quotient form and they should not be equal to zero. I also learned here that you can easily identify whether a function is one-to-one or not if there are no two different elements in x which have the same element in y. If there exists a one-to-one function, then automatically it means that it has its inverse. Inverse function is the reverse of the one-to-one function. Anyhow, I've realized a lot of things after the summative test that I've took. I actually got mental block when I was taking an exam in the "true or false" part and was confused for a moment about the different questions there. I also forgot to double check my answers since I thought that I already clicked the right choice or answer to the question yet I think I overlooked some of the questions there that made me to have a low score. Nevertheless, I've realized that I should study harder when reviewing and avoid the distractions in the environment to efficiently store my knowledge which can help me to avoid being mental blocked in the exact time of the exam. I've also learned that I should always double check my answers twice to avoid regrets later on because of the wrong answer I have clicked in the exam. Thus, with these mistakes that I had done, I've learned and realized that keeping my focus and determination in the exam is a must to have good results in the exam.

REFLECTION:

In this quarter, we've also tackled about the exponential functions and solving these exponential functions respectively. These lessons were also included in the summative test 2. In all honesty, I was really down and shocked because of the situational problems or problem solving related to the exponential functions since it takes really a lot of time for me to analyze and understand the problem clearly. The powerpoint presentations were helpful to me to study even more about the topic. Also, after the discussion of the lesson, I researched and tested myself using the quizzes in the internet to know whether I got the concept right or not. Nonetheless, I did learn a lot of new information in this module since I only thought that exponents are simple yet they are also complex. I've learned that these exponential functions can be and are indeed applicable in everyday life. Besides, there are different properties of exponential functions that depends on their form that helped me easily to determine whether this equation has an asymptote or not, whether they have x-intercept and y-intercept, etc. In order to answer the given problems, I've learned that I should be able to familiarize these properties and the shifts of the exponential function. Furthermore, exponential growth and decay are also tackled here in which you can easily identify whether the function is a growth or decay depending on the variable a and k of the function. Population growth and compound interest topics helped me to realize the importance of learning exponential functions in my life. Population growth has a formula of y = Pe^rt while the compound interest has a formula of C = P(1+r/m)^mt. In the summative exam, I realized that it was a right thing to do to always remember these information to easily solve the problems given in the exam. The mistake I've done in the summative exam was actually because I haven't noticed the increasing word and immediately chose what I answered in the exam. The correct answer also for this problem is actually is y = 50(1.4)^x. Hence, I've learned here that I should read the question carefully before solving and choosing the right answer in the choices so as not to repeat my mistake.

Overall, I definitely learned a lot of new information this first quarter that helped me to expand my knowledge about general mathematics. I've also learned this quarter the logarithmic functions and its properties and how to evaluate them. I did learn too the sketching or graphing of logarithmic functions and their relationship to the exponential functions. Nonetheless, learning the different functions, the techniques, the evaluations, the formulas, the equations and the situation problems were somehow hard yet it was fun. I'm actually glad that I did enjoy these new information while learning these topics knowing that it could help me someday in life.