Comparison Paper
In mathematics, there are many branches of functions. You have Inverse, Linear, Quadratic, Cubic, Periodic, Monotonic, etc. In this paper we will cover Reciprocal and Rational Functions. Both can be plotted on a graph, both have asymptotes, and both have discontinuities. But just because they have a few similarities doesn’t mean that they are all the same. In this paper we will compare and contrast the two functions.

A rational function has the definition of, “Any function which can be written as the ratio of two polynomial functions.” Any time that the denominator is undefined, that means the function is undefined. Since a rational function is set up in a fraction, if the same term is in the numerator and the denominator then those two will “cancel” each other out. When two terms cancel each other out, a hole will occur at the point that both terms cancelled out at. The vertical asymptote is found by the term in the denominator. If you only have (x-2) in the denominator then you will have a vertical asymptote at 2 on the x axis, going vertical. It will be 2 because in the function the vertical asymptote is automatically given a negative sign, so the opposite of whatever your term is. The horizontal is found by any number outside of the fraction.

A reciprocal function can be defined as, “A function that models inverse variations.” Reciprocal functions can be graphed. They usually start at the top or sides of a graph; go inwards towards the origin, then bend past it and leave through the same quadrant that they entered. The x-axis is the horizontal asymptote, and the y-axis is the vertical asymptote. The vertical asymptote is found the same way as the rational function asymptote. As is the horizontal asymptote.

For both the Reciprocal and Rational Functions, you find the asymptotes the same way. You use the same formula, which is y=a/-x-h+k. The vertical asymptote is the opposite value because of the negative sign in the equation. The...

...direct comparison
• You don’t need to write an introduction, so don’t. Leave blank space to come back and write one if you have extra time.
POINT 4 - Direct Comparisons
• 1st Sentence for each body paragraph should be a comparative (a direct comparison sentence)
o Remember you must make Direct Comparisons, (apples to apples) so make it very clear to the reader your comparing in your sentence
▪ Use linking comparative...

...BMAN 31051
International and Comparative Public Management
Guidance notes:
Assignment – 3,000 word essay
Title:
Compare the management of a public service in the UK to that of one other country of your choice. What does the comparison tell you about the factors that shape public management in each country?
Key points to remember:
The tutorial discussions will act as a basis for at least part of the essay.
The tutorials are directly related to the lecture...

...Services compare in many ways, which will be discussed in this paper. However, out of the three the two that compare the most are the AICPA guide and the IMA guide. The AICPA version goes into much more depth and description about each point in comparison to the IMA guide.
Both the AICPA and IMA discuss the importance of integrity, and that avoiding conflict of interest is critical. This is discussed in the public trust section of the AICPA, and in the integrity section of...

...The Comparison of The Sniper and Beware the Dog
This essay is going to compare the two short stories The Sniper and Beware the Dog. I will compare and contrast the differences and similarities of these two stories. I will also explain how they are and probably how I felt about it.
The short stories The Sniper and Beware the Dog is similar because they both are involved in the war and they both lost something that as important to them. They also are similar because...

...each other in some aspect. Hidden in the story, though present, some of Prospero's qualities compare to Caliban's. More obviously though, were the traits of the two that contrasted. Although there are a few things that link Ferdinand and Caliban in comparison, their attitudes on each concept differ greatly.
To begin with, Prospero holds one thing that each character desires. Ferdinand has the fancy for Prospero's daughter, Miranda. Caliban wants his island, which he believes he...

...For a long time, ball mill has been a key equipment for high capacity grinding demand. Nowadays, vertical mill will be active in this field. You must want to know the comparison between them, please read as follows:
1). Higher grinding efficiency. Vertical mill grind material in material bed, engergy cost will be 30% lower than ball mill, as sound engergy and thermal energy will cause energy loss in ball mill.
2). Simpler process flow and less investment need in...

...A Comparison of Multi-Valued Orientation and Two Valued Orientation
Multi-valued orientation and two valued orientation are two completely
different thing. THey compare in only one way. This is the fact that they both
have values. It could be said that a contrastment of the two would be more
useful than a comparison. Two valued orientation is for extremists. Multi-valued
orientation is for things to be ranged on a scale.
Two values orientation is used for the...

...Running Head: SOCIAL COMPARISON THEORY
Introduction
Individuals tend to differentiate significantly in conditions of how they observe and assess their personalities & abilities. There are individuals who observe themselves more positively and those more realistically. Research has exhibited that an individual possessing an enhanced view of one’s self-concept through social comparison tends to lead to extremely favorable outcomes.
Social...

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