Inverse function

• What information did you not know before? I actually did know some of these items, or at least the terms, previously but not in the sense that they were presented to us this week. I was familiar with vertices, edges, and the formal notation of a graph. I didn’t have an appreciation for how graphs could be applied to creating and managing associations with various items by applying them as vertices or edges in a way beyond their representation as numeric coordinates. • What information was…

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…

Greece to the enlightenment in Europe. While it has evolved from the original chord function to a plethora of functions and identities throughout the ages, many of the identities were already known in antiquity and utilized to measure distance and location in the skies. This paper provides a short review of the development of the sine and a short review of the development of the remaining trigonometric functions. The paper ends with an instructional suggestion to teach the fundamental and…

The cosine was developed as the sine of the complement of the angle, and notation for cosine was also varied. The term sinus residuae was used by Viete while Gunter preferred co-sinus in the year 1620. Cavalieri used Si.2, Oughtred used s co arc and Wallis used S [2]. The tangent and cotangent developed out of the need to calculate the height of an object casting a shadow of a certain length, which was of critical importance for the sundial. Thales is known to have used the method of lengths of…

For this curriculum study, I chose third grade mathematics as my unit of study. As far as my objectives go, I would want my students to walk away from this particular section of fractions with the understanding of what a fraction is, the difference between the components of a fraction such as the numerator and denominator, knowing how to identify how many parts of a whole are shaded in, and knowing how to simplify a fraction. As far as my instructional method, I created an original prezi, which…

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…

Results: At the start of the experiment, the initial flow rate was established as 20 ml min-1. This means that there is a steady flow of fluid or blood in your body (in this case, water) at a rate of 20ml min-1. In order to find the final concentration of the Eosin (2,5 mg ml-1) in the “blood” after 60 minutes a calibration curve had to be created by making up seven different solutions of eosin (11,25 μg ml-1) and water to compare it against their absorbance that was calculated in a…