In observing other students trying out along with me (similar to the teachers who observed Maria in chapter 8), it has been valuable to see how they handle these 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; even if we were, it…
of the data. Also, the creation of a trend line allows a correlation between the two subjects to be viewed easier. Trend lines help people accurately determine future outcomes that can come in handy if there is a problem. This is possible because trend lines make it easier to find the slope intercept equation. This equation could be used to find future points in the graph. In this essay I will try to determine who is the best basketball player between Lebron James and Michael Jordan by using a…
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 contrary to what you believed. Another week of nothing being contrary, just new. • How was the Discussion and /or assignment helpful in mastering new information? Both the discussion posts…
Inverse Functions of Trigonometric Functions As high schoolers go their their teenage years of high school they learn from a variety of subjects. From math to science to history, there is a depth of knowledge to be learned. For math 3 and math 4, we are introduced to the world of trigonometry. So far, we have learned that there are currently three main trigonometric functions, cosine, sine, and tangent. But today I want to explore the other side of the trigonometric world, the inverse…
number, it would be said to be a linear function. Common examples of linear function would be distance traveled over time for objects traveling at constant speed; cost of gas in relation to gallons used. Certain situations are linear or not based on whether or not the rate of change is constant or varies. Linear systems are represented by f(x) = mx + b; the slope (m) and the y-intercept (b). In a table that represents a linear function, the input and out puts will be a set of solutions that will…
THE SINE FUNCTION (SIN) Sine function is an odd function. Trigonometric Ratios in a Triangle Definition of sinα in a Triangle is the following statement: For any acute angle α, we draw a right triangle that includes α. The sine of α, abbreviated sin α, is the ratio of the length of the opposite this angle to the length of the hypotenuse of the triangle. If we simplify we get a formula which says: It is shown in a diagram below. We can see immediately that this definition has a weak point. It…
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…
taking seriously. In this unit 5 learning journal, my concentration would be on Exponential and Logarithmic Functions. In section 1, we are told that among all the functions we have examine so far in this course, the exponential and logarithmic functions are the very ones that mostly impact our daily lives the most (Yakir, 2011). In previous learning, we dealt with various functions which includes terms like x2 or x2=3, that is, terms of the form xp where the base of the term, x, varies but the…
‘rand’ function is used. The data is then passed through a QPSK modulator to produce N complex symbols of {±1 , ±1j}. At the receiver, noise is added to the transmitted signal and the resultant signal is then passed through the QPSK demodulator to produce estimates of the transmitted binary data. After that, the demodulator output is compared with the original sequence, and finally an error counter is used to count the number of bit errors. The above procedure is repeated for various values of…
It uses the same x and y values as the graph. I chose to use a positive cosine equation to represent a scenario where Mars is at its aphelion at day 0. This is because a positive cosine function starts at the highest value, where Mars is farthest away from the Sun (aka the aphelion). This equation is a form of the parent function y = a cos(b(x-c)) + d. The “a” value in my equation represents half the distance from the aphelion to the perihelion, or the distance from the aphelion to the…