Rational function

misconceptions and the whole process has been eye-opening with regards to the number of things to consider in my own planning for these “mock” teaching scenarios.Turning to the article on functions by NCTM, I was reminded of my own mathematics learning experiences in middle and high school. I feel as if my understanding of functions (prior to college mathematics) was never fully developed. I’m not sure if we were even shown a “puddle” or “mapping” diagram in any of my secondary math classes;…

Related rates are used in a wide variety of different scenarios from finding how large a spill is increasing, to how fast it may take to empty something. Related rates deal with time, usually have two different variables like height, length, radius, or width; and have something that is changing like area, distance, or volume. In order to solve related rates problems you need to be able to recall or have access to basic geometry formulas like circle, cone, cylinder, rectangle, triangle and…

2.1 The Rational Expectations Hypothesis The rational expectations hypothesis is the hypothesis that, when forming expectations about any variable, people will make optimal use of the available information. This information includes the actual value of certain variables and, more widely, the nature or structure of the world in which people are operating. Let the value a variable ‘y’ takes in period t depend upon, or be a function f (.) of, the value of other variables, x1, x2 and x3 have…

In 1540, a man by the name of Lodovico Ferrari, please be aware that I don’t think his name has anything to do with the sports car, was an Italian mathematician known for discovering the solutions to quartic functions. A quartic function is a function of the form ax^4 + bx^3 +cx^2 +dx+e, where a is a nonzero, which is defined by a polynomial raised to the fourth degree, called quartic polynomial. We will probably go more in depth about these quartic polynomials soon in class. My quartic…

thinking, I have chosen to examine my video from 2:45 – 3:25. During this time, I asked students for their answers to the problem given to them and their reasoning for this answer. In essence, I was hoping to target students’ knowledge of inverse functions and how they applied it to solving a situational problem. More specifically, if they were able to find the error in a solution of an inverse algebraic problem and explain their reasoning for this error. Moreover, once a student was able to…

Every person has their own perspective of ethics. Each human being has their own set of moral rules, or beliefs, that guide them in their behavior. Though there are quite a few philosophical theories to which a person may rest their convictions, ethical egoism is among the ones most debated. In this paper, I will argue as to why ethical egoism is not a good philosophy to follow. Ethical egoism is the normative theory that it is always morally right to encourage a person's own good. A normative…

allowed us to construct a national income model. We used figures for 2014. UK National Income model approximations The variables we need include: • A consumption function, C = a + b(Y-T) • An import demand function, M = k + mY • Exogenous variables, representing investment, I*, exports, X*, government expenditure, G* • A tax revenue function, T = tY + T* • Equilibrium condition for Y National income in the uk In 2014 the GDP in the UK came to $2522.26 Billion. We will use this…

It is important in children’s cognitive development and with their success in school. Executive functions are used to organize and act on information. Working memory is one executive function. This skill is the ability to carry information in mind for the purpose of completing a task. Working memory is like your mental sticky note. When I was in fifth grade my classmates and I were learning how…

There are several areas in the natural world where the process of exponential decay arises from random processes. Whenever a material decays at a rate in proportion to its amount, this material represents the process of exponential decay. Exponential decay can be described using the mathematical model y=a×e^(-bx). A prominent example of naturally occurring random exponential decay is the process of radioactive decay. Some isotopes of nature are considered radioactive due to a specific…

People are pretty selfish and independent huh? Damn, then there's people that puts others first. Individualistic society is comprised of a group of independent people that prioritize furthering one’s own self-interests. On the other hand, collectivist societies put society’s well-being over an individuals’. In the novel “Animal Farm” by George Orwell there is a farm taken control by animals and where animals believe they were equal. The two main character’s of “Animal Farm” are two pigs named…