Incest, Murder, And Suicide - 1424 Words

Incest, murder, and suicide; many readers regard Oedipus the King as a story of a tragic hero unable to alter his course of fate. Fate is defined as â€Å"a power that is believed to control what happens in the future† (Merriam-Webster). It is believed in Greek Mythology â€Å"that many aspects of a person’s life were determined by the three mythical women known as Fates. These were three sister goddesses that appeared in Greek and Roman mythology and were believed to have â€Å"spun out† a child’s destiny at birth. They determined when life began, when it ended, and everything in between. At the birth of each man they appeared spinning, measuring, and cutting the thread of life. However not everything was inflexible or predetermined. A man destined to become a great warrior one day cold still choose what he wanted to do on any given day. The gods cold simply intervene with decisions that could be helpful or harmful. In a sense, they controlled the metaph orical life of every mortal born† (The Three Fates: Destiny s Deities of Ancient Greece and Rome). Oracles or prophets were often times used to help see into the future in an effort to possibly change the outcome. However, fate cannot be avoided or altered even if using free will, it is who we are or who we are meant to be, it is set into motion the day we are born. Websters dictionary defines free will as â€Å"freedom of humans to make choices that are not determined by prior causes or by divine intervention† (Merriam-Webster). As theShow MoreRelatedRelativism and Morality871 Words   |  4 Pagesthat should never be considered as options. The twelve areas which Goodman addresses include the following: (1) genocide, politically induced famine, and germ warfare; (2) terrorism, hostage taking, and child warriors; (3) slavery, polygamy, and incest; and (4) rape and female genital cutting. According to Goodman, these practices are simply and absolutely wrong under any circumstances. I think that most of us would agree with Goodman that these twelve acts are absolute wrongs, and their continuedRead MoreA Case On Proactive Death Such As Physician Assisted Suicide763 Words   |  4 PagesThis essay will reveal different case studies on proactive death such as physician-assisted suicide, pro-life principles to natural death emphasis on life at conception and the circumstances under which proactive efforts are permissible. Physicians assisting in suicide deaths are not productive in this area because some not trained in this field of expertise. Moll assert, doctors, are of little help. They have no training in how to discuss end-of-life issues with families and patients, so they avoidRead MoreChristianity in Shakespears Hamlet1148 Words   |  5 Pagesof the time when Shakespeare writes the play. Reformation and Renaissance opinions are reflected throughout. Shakespeare deals with very controversial attitudes and religious questions dealing with death, the existence of purgatory, morality, murder, suicide and marriage in his play Hamlet. It is obvious throughout the play that Hamlet’s life is guided by his faith and his religious beliefs. At first, Hamlet sees the ghost of his dead father and vows to avenge his death. â€Å"Christianity forbidsRead MoreEssay on Abortion: More Harm than Good1209 Words   |  5 Pagesabortion she will not have to bring an unwanted baby into the world, but is it really a relief? Abortion brings along with it many destructive packages. Packages of murder, emotional and psychological effects along with medical problems. So, Now your thinking Abortion isnt murder, the baby is not even born yet. Well Abortion is murder. An innocent human life is brutally murdered every 22 seconds in the United States. That is a lot of babies being killed every day, and thats just in the United StatesRead MoreShould Abortion Be Legal?1324 Words   |  6 Pagesthat abortion is murder, and that under no circumstances should it be legal, permissible or justified. Abortion is a topic that is affecting society strongly at the time, as it has been for decades. Many people believe that abortion should be legal if the mother chooses to have one, or that it should only be legal in the case of incest or rape. Other people believe that it is never acceptable and should be banned everywhere in the world. I believe it is always wrong and murder, and should neverRead MoreTo Kill a Mockingbird by Harper Lee1185 Words   |  5 PagesTo Kill a Mockingbird is a novel that takes place during the depression and in the Deep South wh ere racial discrimination is prominent. Hamlet is a tragic play, written about the sixteenth and seventeenth centuries, involving incest, murder, and dishonesty. The above literatures are written during different periods of time and are contrastive in numerous aspects. However, both literatures are comprised of numerous scenes where the main characters deal with situations that test their morality andRead MoreHamlets Madness Essay1147 Words   |  5 Pagespoint of obsession, leading him into isolation. He can no longer distinguish fantasy from reality in turn motivating his impulsive behavior and stripping him of his integrity. Shakespeare has Hamlet feign madness however, as a result of his father’s murder, the obsession to plot revenge on Claudius, and the neglected love from the women in his life his behavior is so manic that the audience could assume he is genuinely mad. It is clear that Hamlet has difficulty accepting the death of his father, heRead MoreHamlet Essay : Will Hamlet Be Sent To Hell?1440 Words   |  6 Pagesintentionally due their intent to decease his life. Because Hamlet killed Polonius his daughter committed suicide. He had caused Ophelias death. Above all his murders had motive, but still he’s innocence wins over because he was seeking justice. I’ll be briefing why Hamlet will be redeemed from hell using all the murders he had caused whether it was an accident or mistake. In addition to Hamlet’s first murder is Polonius. It had occurred in Gertrudes room after Hamlet’s play had been auditioned. It wasRead MoreIs Oedipus Guilty Essay1249 Words   |  5 Pagesshould be held liable for his crimes of patricide (killing his father) and marrying and having a sexual relationship his mother. Oedipus knew nothing about the past of Thebes however, what was done cannot be taken back. His actions were wrong because incest is unethical, and murdering someone is a crime. He guilty because guilt lies in the act of doing, not in intention. In addition to the prophecy, Oedipus is also guilty of hubris because he displayed excessive pride. The choice was his, and this accountsRead More Aspects of Life in Hamlet, Prince of Denmark and Trifles Essay2332 Words   |  10 Pagesplay, Trifles, women are strong in character, protective of one another, and in charge of the situation, unlike Gertrude. Therefore, both Shakespeare and Gaspell have similar aspects of portrayal of the role of women, murder, and loyalty; and different aspects such as incest, suicide, and revenge. First, in the play, Hamlet, the males are depicted as dominant, strong, and rational; and the females are portrayed by opposing traits such as passive, accepting, hesitant, frail, and emotional

The Flight Attendant Training Program - 757 Words

Charles Lindbergh flew the first American Airlines flight on April 15, 1926 carrying U.S. mail from St. Louis, Missouri to Chicago, Illinois (American Airlines). American Airlines flew United States mail routes for about eight years until C.R. Smith and Donald Douglas created the DC-3 plane that would change the airline industry. The DC-3 flew in service from New York to Chicago (American Airlines). Over the years the company began to grow what it is today. American Airlines grew from engineering the DC-3 to the DC-7 and eventually created new flight planes that would be able to take passengers all over the United States and eventually overseas. American Airlines was the first airline to create a specialized flight attendant training program (American Airlines). The airline knew the importance of keeping its passengers comfortable during their flight. Finally, on October 16, 2015 U.S. Airways flew its last flight and on October 17, 2015 U.S. Airways and American Airlines began to ope rate under one company. The key issues that are behind the American Airlines and U.S. Airways merger is that when it all comes down to it is that once these two companies are combines they will be better able to offer its customers better options according to Thomas C. Lawton (2013). However, since two companies are becoming one the critics will argue that there will be less competition in the airline industry especially since there seem only to be four major airlines now, Delta, AmericanShow MoreRelatedEducation And Training Within The Aviation Industry1635 Words   |  7 PagesEducation and Training within the Aviation Industry Kamiana K. Jardine Embry-Riddle Aeronautical University Management 314: Human Resource Management Professor Trish Poznick Abstract This essay examines how companies are meeting the demand for a highly skilled work force through the integration of technology and higher education as well as adaptation policies enacted by the FAA. It will examine the current market as well as forecast the next few years within the industry and how this will affectRead MoreA Career as a Flight Attendant1182 Words   |  5 Pagespossibility to some people to travel for free? Flight attendant is the wonderful career that enables people to travel round-the-world in a month without spending money. Surprisingly, according to Wallner’s (2000) book â€Å"Flight Attendant†, historically, the first flight attendants were men. They were called couriers and they were sons of ship, railroad, and other business owners who supported airlines financially. However, nowadays, flight attendants are men and women. The job requirements might beRead MoreExecutive Summary1470 Words   |  6 Pages Jeff Heisey. Adam addressed the United ME C and provided several updates on issues currently impacting Flight Attendants. He gave a brief overview of the state of the airline industry, including the announcement of John Slater who is the successor of Sam Risoli. United Master Executive Council (MEC) Secretary-Treasurer, Jeff Heisey followed with an update on the Inflight Safety Action Program (ISAP) reporting process and the shifting of flying around the system. AFA is no longer supporting ISAPRead MoreAircraft Engine Specialists Are Responsible For Repair And Replace Worn Cars1265 Words   |  6 Pagesknowledge of physics, mathematics, public safety and security, computers and electronics, design technics, transportation methods, law, government and jurisprudence, and telecommunications. They should be able to provide instructional method and training. 3. Decision-making: The individuals should have the judgement and decision making skills. It is very technical job and some decisions are made on spot. Therefore, the Aircraft Engine Specialists should be able to handle different serious situationRead MoreThe Homeland Security Act Of 20021562 Words   |  7 Pagesthat the DHS accomplishes the mission through inspections. In addition, the Inspector General ensures the programs set in place by congress are operating effectively. The mission of the Inspector general is â€Å"To conduct independent audits, inspections, evaluations, and investigations to promote economy and efficiency and to prevent and detect waste, fraud, abuse, and mismanagement in the programs and operations of the Department and the Broadcasting Board of Governors†(Office of Inspector General, nRead MoreJetBlue Airways Case Study1730 Words   |  7 Pagesgrows Though industry for start-ups Difficult to hire quickly at high standards No structures for building team and participation as they grow Lack of standardization in HR policies could be source of inequity, division Flight attendants turnover could create high training costs, poor service Jet Blue Strategy: Low cost, low price JFK – under-served markets and beachhead for protected revenues stream Increase demand through low fares High asset utilization High productivity (people) PeopleRead MoreAnalysis Of Southwest Airlines Crazy Recipe For Business And Personal Success By Kevin L. Freiberg1170 Words   |  5 Pagesand it promoted a high work spirit as well as created a playful feeling while working. Consequently, it also drove their employees to be creative at work. One of the examples is the creative approach while flight attendants were giving games, poems, skits, or songs to their customers in a flight. The sociability in Southwest also described as a family relationship. The organization realized the important of having a strong relationship among their members and treated them as a family. In additionRead MoreWhy Southwest Is A Values Based Firm Looks Like1465 Words   |  6 PagesSouthwest’s approaches to business are based on fun, trust, community, and family. For example, at Southwest, there is little cross training except for only two formal teams: the marketing and reservations department. This means that Southwest promotes mingling with the employees for informal networking and helping each other out, in spite of their job assignments. â€Å"Flight attendants and pilots help clean the aircraft or check passengers in at the gate. Some employees accompanied an elderly passenger to theRead MoreHistory Of Southwest Airlines By Rollin King And Herb Kelleher920 Words   |  4 Pagessame day, SWA was offered three 737-200s by Boeing. During 1971, southwest airlines began scheduled flights from Dallas to Houston and San Antonio with a $20 one-way fares. In Addition, on July 09, 1972, southwest introduced Executive Class Service fares with a fare increase and complimentary cocktails. On the other hand, on October 01, 1974, SWA introduced a new uniform for their Flight Attendant, consisting of an orange blouse with white dots, an orange hot pants and an aviator jacket. On theRead MoreSouthwest Airlines (a)1324 Words   |  6 Pages(hence, the acronym, also its stock ticker symbol) in 1971. Before its first flight, LUV ha d to fight fierce battles with the big carriers which resulted in a law amendment, allowing direct flights to Love Field only from within Texas and its 4 contiguous states (â€Å"Wright Amendment†), which meant that all long distant flights needed separate ticket purchases. Initially, LUV gained attention by putting its flight attendants in hot pants and an advertising campaign themed around love. Over the years

Comparison Paragraph free essay sample

In the novel Or-pix and Crake by Margaret Atwood, Crake is an example f a character who displays abusive power. Crake created the Plausibly pill, a pill that would eventually wipe out the whole human race for his own selfish wants. He thought that the entire human race was the main source of destruction in the world. Crake thought people were all trapped in their own selfish desires, he believed they were unworthy of life. So when he designed the Plausibly pill that would create an airborne disease and kill off the entire human race except for one, Jimmy.Crake was playing God and put the fate of he entire human race into his own hands, which ultimately ended in the apocalypse. After the apocalypse occurred the whole world was destroyed, Crake eliminated Jimmy from his plan to wipe out the race. Left him to fend for himself and take care of his creation, the Crackers. We will write a custom essay sample on Comparison Paragraph or any similar topic specifically for you Do Not WasteYour Time HIRE WRITER Only 13.90 / page Jimmy was left in all the chaos and is ultimately suffering alone in misery and despair replaying his old reality over and over throughout his thoughts.Similarly in the movie The Quiet American directed by Phillip Nonce, the character Eldon Pyle kills many villains on an attack placing dialectic, an explosive material used in creating bombs into cars blowing up a whole Vietnamese town. This was a direct order by Pyle for his own selfish desires as well. Pyle had ordered General These men to make the hit, and then blame it on the communists. He had wanted the hit to look like the communist had done it to make them look bad in the eyes of the public. Pyle made the hit and did not even have remorse for the many innocent civilians he had just killed.He wanted the communists out of Korea and he would do anything, even if that meant killing innocents to get what he wanted. In doing this he caused a lot of grief and suffering to the people around him, the many people who lost loved ones in the bombing, and Phonon. Pyle had made a promise to Phonon that he would take her to the United States with him to ensure she is safe and secure but after his death she was left trapped in Korea to suffer during the war. In both of these examples the characters display abusive power, both ending in tragedy and destruction to the many around them.

The Devil In The Shape Of A Woman Essays - Witchcraft, Witch Trials

The Devil In The Shape Of A Woman Karlsen, Carol F. The Devil in the Shape of a Woman. New York: Vintage Books, 1987. Carol Karlsen was born in 1940. She is currently a professor in the history department a the University of Michigan. A graduate of Yale University (Ph.D, 1980), she has taught history and women's study courses at Union College and Bard College. In this book Carol Karlsen reveals the social construction of witchcraft in 17th century New England, and brings forth the portrait of gender in the New England Society. The books thesis is based on why a person was accused of being a witch and the relative circumstances thereof. Marital status, sex, community standing, wealth, and relationships with others all play an important part of a person chances of being accused of being a witch. Karlsen's words make for a richly detailed portrait of the women who were prosecuted as witches. The witch hunting hysteria seized New England in the late seventeenth century. Why were those and other women likely witches? Why were certain people vulnerable to accusations of witchcraft and possession? These are the questions answered in this book. The book focuses mainly on the time period between 1620-1725, give or take a few years. Colonial New England is the setting. The author puts great emphasis on towns where witch trials were predominate. In these towns religion, social status and wealth seemed to be important to most people. The courts in these towns relied on religion as much as the law to run their trials. Colonial New England in the early 1600's was in a state of decision. A lot of the beliefs about witchcraft came from the policy's of England, the mother country. During the early years of settlement, puritans in Massachusetts Bay were uncertain about how to translate their sexual beliefs into public policy. As early as 1651, Massachusetts passed their first adultery law. In the ensuing years ahead the Massachusetts magistrates articulate more precisely the form of punishment appropriate for different crimes. Even though these laws were written to be fair to all, the magistrates and clergy delegated punishment by who was being punished. This type of reasoning was typical in New England, and set the stage for the witch trials. The content of The Devil in the Shape of a Woman is broken down into sections, by time and place. There are several charts in the book showing the relationship of gender, age, wealth and place on how an accused witch was treated. Most show that women were targeted at a greater extent than anybody. Most observers now agree that witches in the villages and towns of the late Sixteenth and Seventeenth Century New England tended to be poor. They were usually not the poorest women in the community, but the moderately poor. Karlsen tries to show that a woman who was vulnerable was most likely to be accused of being a witch. Even women who had gained wealth because of the death of a husband were prime candidates. Promiscuity was also known to be a reason for being accused accused of witchery. Marital problems often led to a disgruntled husband screaming witch. A woman who could not conceive a child, or one who would not give into her husband's wishes could easily be accused. Karlsen touches on the events leading up to the witch trials of Salem in almost every chapter. The events which led to the witch trial actually occurred in what is now the town of Danvers, then a parish of Salem Town, know as Salem Village. Launching the hysteria was the bizarre, seemingly inexplicable behavior of two young girls; the daughter, Betty, and the niece, Abigail Williams, of the Salem Village minister, Reverend Samuel Parris. These girls were experimenting with magic. They used an improvised crystal ball to try to see their futures. A few days later they began to have fits and exhibited other manifestations of possession, which spread to other females in the village. By the time the hysteria had spent itself, twenty four persons had died. Nineteen were hanged on Gallows Hills in Salem Town. The rest died in prison. The references for Karlsen's work are lengthy. Several documents still exist showing land transfers

Braydon Waller Essays (488 words) - English-language Films, 9 To 5

Braydon Waller Humanities Professor Hughes December 3, 2017 Nine to five the musical Nine to five the musical is a musical based around a 1980 movie of the same name that has music and lyrics by Dolly Parton in it. It's a funny and energetic play about friends and revenge. Three coworkers come up with a plan to get back at their egotistic boss but they find out there is nothing they can do about it. Personally I thought the play was funny and it was actually pretty good. It was very good about keeping with the themes of what the play had, like the daily workplace struggles and what else goes on in the workplace. It keeps the theme of friendship in work and working together to get back at the boss, also kept with the comedy theme even with some seriousness mixed in the play. The play seems to me to be very creative with how everything throughout the play works. The dialogue, scenes, set, and characters for it are very creative and interesting with how it all works together. There's violet the working mom, Doralee a country girl, Judy the new employee a nd finally the boss Franklin Hart. One of the first things Franklin does is make them get his coffee which just shows just how he is, also with all the flirting he does with them. The play is very well acted with all the actors seeming to work together in unison to understand the play better and it helped to make the play even better than it already was. The production of the play one hundred percent made it easier to understand, I had really no understanding what the play was fully about, but how it was produced definitely made it easier to watch. With just how the director, character and everyone involved in the play made that much easier to understand. The overall language of the play was good and the actors made every line clear and with great emotion. They made the play stay with the theme with how they acted, they kept with the seriousness of the workplace and the comedy of it too, and they made it all tie together. With how the actors portrayed the characters an d the scenes they helped make a better understanding about nine to five the musical for the audience. There was a broad concept on the stage and costumes to paint a better picture of the characters, theme, and concepts of the play. They definitely made it look and feel like a workplace comedy on the stage. The director and actors overall made the personalities and actions of the characters come out through their position onstage. Overall the play was very entertaining and funny to watch. I was impressed on acting, the portrayal of the characters, and the director making everything play together to make it entertaining for the entire audience.

Functions on SAT Math Linear, Quadratic, and Algebraic

Functions on SAT Math Linear, Quadratic, and Algebraic SAT / ACT Prep Online Guides and Tips SAT functions have the dubious honor of being one of the trickiest topics on the SAT math section. Luckily, this is not because function problems are inherently more difficult to solve than any other math problem, but because most students have simply not dealt with functions as much as they have other SAT math topics. This means that the difference between missing points on this seemingly tricky topic and acing them is simply a matter of practice and familiarization. And considering that function problems generally show up on average of three to four times per test, you will be able to pick up several more SAT math points once you know the rules and workings of functions. This will be your complete guide to SAT functions. We'll walk you through exactly what functions mean, how to use, manipulate, and identify them, and exactly what kind of function problems you'll see on the SAT. What Are Functions and How Do They Work? Functions are a way to describe the relationship between inputs and outputs, whether in graph form or equation form. It may help to think of functions like an assembly line or like a recipe- input eggs, butter, and flour, and the output is a cake. Most often you'll see functions written as $f(x) =$ an equation, wherein the equation can be as complex as a multivariable expression or as simple as an integer. Examples of functions: $f(x) = 6$ $f(x) = 5x − 12$ $f(x) = x^2 + 2x − 4$ Functions can always be graphed and different kinds of functions will produce different looking graphs. On a standard coordinate graph with axes of $x$ and $y$, the input of the graph will be the $x$ value and the output will be the $y$ value. Each input ($x$ value) can produce only one output, but one output can have multiple inputs. In other words, multiple inputs may produce the same output. One way to remember this is that you can have "many to one" (many inputs to one output), but NOT "one to many" (one input to many outputs). This means that a function graph can have potentially many $x$-intercepts, but only one $y$-intercept. (Why? Because when the input is $x=0$, there can only be one output, or $y$ value.) A function with multiple $x$-intercepts. You can always test whether a graph is a function graph using this understanding of inputs to outputs. If you use the "vertical line test," you can see when a graph is a function or not, as a function graph will NOT hit more than one point on any vertical line. No matter where we draw a vertical line on our function, it will only intersect with the graph a maximum of one time. The vertical line test applies to every type of function, no matter how "odd" looking. Even "strange-looking" functions will always pass the vertical line test. But any graph that fails the vertical line test (by intersecting with the vertical line more than once) is automatically NOT a function. This graph is NOT a function, as it fails the vertical line test. Too many obstacles in the way of the ascent works out as well for functions as it does for real life (which is to say: not well at all). Function Terms and Definitions Now that we've seen what functions do, let's talk about the pieces of a function. Functions are presented either by their equations, their tables, or by their graphs (called the "graph of the function"). Let's look at a sample function equation and break it down into its components. An example of a function: $f(x) = x^2 + 5$ $f$ is the name of the function (Note: we can call our function other names than $f$. This function is called $f$, but you may see functions written as $h(x)$, $g(x)$, $r(x)$, or anything else.) $(x)$ is the input (Note: in this case our input is called $x$, but we can call our input anything. $f(q)$ or $f(\strawberries)$ are both functions with the inputs of $q$ and strawberries, respectively.) $x^2 + 5$ gives us the output once we plug in the input value of $x$. An ordered pair is the coupling of a particular input with its output for any given function. So for the example function $f(x) = x^2 + 5$, with an input of 3, we can have an ordered pair of: $f(x) = x^2 + 5$ $f(3) = 3^2 + 5$ $f(3) = 9+5$ $f(3) = 14$ So our ordered pair is $(3, 14)$. Ordered pairs also act as coordinates, so we can use them to graph our function. Now that we understand our function ingredients, let's see how we can put them together. Different Types of Functions We saw before that functions can have all sorts of different equations for their output. Let's look at how these equations shape their corresponding graphs. Linear Functions A linear function makes a graph of a straight line. This means that, if you have a variable on the output side of the function, it cannot be raised to a power higher than 1. Why is this true? Because $x^2$ can give you a single output for two different inputs of $x$. Both $−3^2$ and $3^2$ equal 9, which means the graph cannot be a straight line. Examples of linear functions: $f(x) = x − 12$ $f(x) = 4$ $f(x) = 6x + 40$ Quadratic Functions A quadratic function makes a graph of a parabola, which means it is a graph that curves to open either up or down. It also means that our output variable will always be squared. The reason our variable must be squared (not cubed, not taken to the power of 1, etc.) is for the same reason that a linear function cannot be squared- because two input values can be squared to produce the same output. For example, remember that $3^2$ and $(−3)^2$ both equal 9. Thus we have two input values- a positive and a negative- that give us the same output value. This gives us our curve. (Note: a parabola cannot open side to side because it would have to cross the $y$-axis more than once. This, as we've already established, would mean it was not a function.) This is NOT a quadratic function, as it fails the vertical line test. A quadratic function is often written as: $f(x) = ax^2 + bx + c$ The $\bi a$ value tells us how the parabola is shaped and the direction in which it opens. A positive $\bi a$ gives us a parabola that opens upwards. A negative $\bi a$ gives us a parabola that opens downwards. A large $\bi a$ value gives us a skinny parabola. A small $\bi a$ value gives us a wide parabola. The $\bi b$ value tells us where the vertex of the parabola is, left or right of the origin. A positive $\bi b$ puts the vertex of the parabola left of the origin. A negative $\bi b$ puts the vertex of the parabola right of the origin. The $\bi c$ value gives us the $y$-intercept of the parabola. This is wherever the graph hits the $y$-axis (and will only ever be one point). (Note: when $b=0$, the $y$-intercept will also be the location of the vertex of the parabola.) Don't worry if this seems like a lot to memorize right now- with practice, understanding function problems and their components will become second nature. Want to learn more about the SAT but tired of reading blog articles? Then you'll love our free, SAT prep livestreams. Designed and led by PrepScholar SAT experts, these live video events are a great resource for students and parents looking to learn more about the SAT and SAT prep. Click on the button below to register for one of our livestreams today! Typical Function Problems SAT function problems will always test you on whether or not you properly understand the relationship between inputs and outputs. These questions will generally fall into four question types: #1: Functions with given equations #2: Functions with graphs #3: Functions with tables #4: Nested functions There may be some overlap between the three categories, but these are the main themes you'll be tested on when it comes to functions. Let's look at some real SAT math examples of each type. Function Equations A function equation problem will give you a function in equation form and then ask you to use one or more inputs to find the output (or elements of the output). In order to find a particular output, we must plug in our given input for $x$ into our equation (the output). So if we want to find $f(2)$ for the equation $f(x) = x + 3$, we would plug in 2 for $x$. $f(x) = x + 3$ $f(2) = 2 + 3$ $f(2) = 5$ So, when our input $(x)$ is 2, our output $(y)$ is 5. Now let's look at a real SAT example of this type: $g(x)=ax^2+24$ For the function $g$ defined above, $a$ is a constant and $g(4)=8$. What is the value of $g(-4)$? A) 8 B) 0 C) -1 D) -8 We can start this problem by solving for the value of $a$. Since $g(4) = 8$, substituting 4 for $x$ and 8 for $g(x)$ gives us $8= a(4)^2 + 24 = 16a + 24$. Solving this equation gives us $a=-1$. Next, plug that value of $a$ into the function equation to get $g(x)=-x^2 +24$ To find $g(-4)$, we plug in -4 for $x$. From this we get $g(-4)=-(-4)^2 + 24$ $g(-4)= -16 + 24$ $g(-4)=8$ Our final answer is A, 8. Function Graphs A function graph question will provide you with an already graphed function and ask you any number of questions about it. These questions will generally ask you to identify specific elements of the graph or have you find the equation of the function from the graph. So long as you understand that $x$ is your input and that your equation is your output, $y$, then these types of questions will not be as tricky as they appear. The minimum value of a function corresponds to the $y$-coordinate of the point on the graph where it's lowest on the $y$-axis. Looking at the graph, we can see the function's lowest point on the $y$-axis occurs at $(-3,-2)$. Since we're looking for the value of $x$ when the function is at it's minimum, we need the x-coordinate, which is -3. So our final answer is B, -3. Function Tables The third way you may see a function is in its table. You will be given a table of values both for the input and the output and then asked to either find the equation of the function or the graph of the function. Oftentimes the best strategy for these types of questions is to plug in answers to make our lives simpler. This way, we don't have to actually find the equation on our own- we can simply test which answer choices match the inputs and outputs we are given in our table. Let's test the second ordered pair, $(3,13)$ with each answer option. For the correct answer, when we plug the $x$-value (3) into the equation, we'll end up with the correct $y$-value (13). A) $f(x) = 2(3) +3 = 9$. This equation is incorrect since 9 doesn't equal 13. B) $f(x) =3(3) +2 = 1$. This equation is also incorrect. C) $f(x) = 4(3) +1=13$. It's a match! This equation is correct so far. D) $f(x)= 5(3)= 15$. This equation is also incorrect. It looks like C is the correct answer choice, but let's plug the first and third ordered pairs in to make sure. For the first ordered pair $(1,5)$: $f(x) = 4(1) +1=5$ That's correct! For the third ordered pair $(5,21)$ $f(x) = 4(5) +1=21$ That's also correct! Our final answer is C, $f(x) = 4x +1$ Nested Functions The final type of function problem you might encounter on the SAT is called a "nested" function. Basically, this is an equation within an equation. In order to solve these types of questions, think of them in terms of your order of operations. You must always work from the inside out, so you must first find the output for your innermost function. Once you've found the output of your innermost function, you can use that result as the input of the outer function. Let's look at this in action to make more sense of this process. What is $f(g(x−2))$ when $f(x) = x^2 − 6$ and $g(x) = 3x + 4?$ A. $3x − 2$ B. $3x^2 + 12x − 6$ C. $9x^2 + 24x + 10$ D. $9x^2 − 12x + 4$ E. $9x^2 − 12x − 2$ Because $g(x)$ is nested the deepest, we must find its output before we can find $f(g(x−2))$. Instead of a number for $x$, we are given another equation. Though this may look different from earlier problems, the principle is exactly the same- replace whatever input we have for the variable in the output equation. $g(x) = 3x + 4$ $g(x−2) = 3(x−2) + 4$ $g(x−2) = 3x − 6 + 4$ $g(x−2) = 3x − 2$ So our output of $g(x−2)$ is $3x−2$. Again, this is an equation and not an integer, but it still works as an output. Now we must finish the problem by using this output of $g(x)$ as the input of $f(x)$. (Why do we do this? Because we are finding $f(g(x))$, which positions the result/output of $g(x)$ as the input of $f(x)$.) $f(x) = x^2 − 6$ $f(g(x−2)) = (3x−2)^2 − 6$ Now, we have a bit of a complication here in that we must square an equation. If you remember your exponent rules, you know you cannot simply distribute the square across the elements of the equation; you must square the entire expression. So let's take a moment to expand $(3x−2)^2$ before we find the solution for the entire equation. $(3x − 2)^2$ $(3x − 2)(3x − 2)$ $(3x*3x) + (3x*-2) + (−2*3x) + (−2*-2)$ $9x^2 − 6x − 6x + 4$ $9x^2 − 12x + 4$ Now, let us add this expanded form of the equation back into the output. $f(g(x−2)) = (9x^2 − 12x + 4) − 6$ $f(g(x−2)) = 9x^2 − 12x − 2$ So our final solution for $f(g(x−2))$ is $9x^2 − 12x − 2$. Our final answer is E, $9x^2 − 12x − 2$. Functions within functions, dreams within dreams. Make sure not to lose yourself along the way. Strategies for Solving Function Problems Now that you've seen all the different kinds of function problems in action, let's look at some tips and strategies for solving function problems of various types. For clarity, we've split these strategies into multiple sections- tips for all function problems and tips for function problems by type. So let's look at each strategy. Strategies for All Function Problems: #1: Keep careful track of all your pieces and write everything down Though it may seem obvious, in the heat of the moment it can be far too easy to confuse your negatives and positives or misplace which piece of your function (or graph or table) is your input and which is your output. Parenthesis are crucial. The creators of the SAT know how easy it is to get pieces of your function equations confused and mixed around (especially when your input is also an equation), so keep a sharp eye on all your moving pieces and don't try to do function problems in your head. #2: Use PIA and PIN as necessary As we saw in our function table problem above, it can save a good deal of effort and energy to use the strategy of plugging in answers. You can also use the technique of plugging in your own numbers to test out points on function graphs, work with any variable function equation, or work with nested functions with variables. For instance, let's look at our earlier nested function problem using PIN. (Remember- most any time a problem has variables in the answer choices, you can use PIN). What is $f(g(x−2))$ when $f(x)= x^2 − 6$ and $g(x) = 3x + 4?$ A. $3x^2 + 24x − 2$ B. $3x^2 + 12x − 6$ C. $9x^2 − 24x + 10$ D. $9x^2 − 12x + 4$ E. $9x^2 − 12x − 2$ If we remember how nested functions work (that we always work inside out), then we can plug in our own number for $x$ in the function $g(x−2)$. That way, we won't have to work with variables and can use real numbers instead. So let us say that the $x$ is the $g(x−2)$ function is 5. (Why 5? Why not!) Now $x−2$ will be $5−3$, or 3. This means $g(x−2)$ will be $g(3)$. $g(x−2) = 3x + 4$ $g(3) = 3(3) + 4$ $g(3) = 9 + 4$ $g(3) = 13$ Now, let us plug this number as the value for our $g(x−2)$ function into our nested function $f(g(x−2))$. $f(x) = x^2 − 6$ $f(g(3)) = (13)^2 − 6$ $f(g(3)) = 169 − 6$ $f(g(3)) = 163$ Finally, let us test our answer choices to see which one matches our found answer of 163. Let us, as usual when using PIA or PIN, start in the middle with answer choice C. $9x^2 − 24x + 10$ Now, we replace our $x$ value with the $x$ value we chose originally- 5. $9x^2 − 24x + 10$ $9(5)^2 − 24(5) + 10$ $9(25) − 120 + 10$ $225 − 120 + 10$ 5 Unfortunately, this number is too small. Let us try answer choice D instead. $9x^2 − 12x + 4$ $9(5)^2 − 12(5) + 4$ $9(25) − 60 + 4$ $225 − 60 + 4$ $165 + 4$ 169 This value is still too large, but we can see that it is awfully close to the final answer we want. Just by looking over our answer choices, we can see that answer choice E is exactly the same expression as answer choice D, except for the final integer value. If we were to subtract 2 from 165 instead of adding 4 (as we did with answer choice D), we would get our final answer of 163. As you can see. $9x^2 − 12x − 2$ $9(5)^2 − 12(5) − 2$ $9(25) − 60 − 2$ $225 − 60 − 2$ $165 − 2$ 163 So our final answer is E, $9x^2 − 12x − 2$. #3: Practice, practice, practice Finally, the only way to get truly comfortable with any math topic is to practice as many different kinds of questions on that topic as you can. If functions are a weak area for you, then be sure to seek out more practice questions. For Function Graphs and Tables: #1: Start by finding the $\bi y$-intercept Generally, the easiest place to begin when working with function graphs and tables is by finding the y-intercept. From there, you can often eliminate several different answer choices that do not match our graph or our equation (as we did in our earlier examples). The y-intercept is almost always the easiest piece to find, so it's always a good place to begin. #2: Test your equation against multiple ordered pairs It is always a good idea to find two or more points (ordered pairs) of your functions and test them against a potential function equation. Sometimes one ordered pair works for your graph and a second does not. You must match the equation to the graph (or the equation to the table) that works for every coordinate point/ordered pair, not just one or two. For Function Equations and Nested Equations: #1: Always work inside out Nested functions can look beastly and difficult, but take them piece by piece. Work out the equation in the center and then build outwards slowly, so as not to get any of your variables or equations mixed up. #2: Remember to FOIL It is quite common for SAT to make you square an equation. This is because many students get these types of questions wrong and distribute their exponents instead of squaring the entire expression. If you don't properly FOIL, then you will get these questions wrong. Whenever possible, try not to let yourself lose points due to these kinds of careless errors. For instance, let's say that you must square an expression. Square the expression $x + 3$. We are told to square the entire expression, so we would say: $(x + 3)^2$ Now you must FOIL this out properly. $(x + 3)(x + 3)$ $(x*x)+(3*x)+(3*x)+(3*3)$ $x^2 + 3x + 3x + 9$ $x^2 + 6x + 9$ The final expression, once you have squared $x + 3$, is: $x^2 + 6x + 9.$ (Note: It is a common error for students to distribute the square and say: $(x + 3)^2 = x^2 + 9$ but this is wrong. Do not fall into this kind of trap!) You're all leveled-up- time to fight the big boss and put knowledge to action! Test Your Knowledge Now let's put your function knowledge to the test against real SAT math problems. 1. Let the function $f$ be defined bye $f(x)=5x-2a$, where $a$ is a constant. If $f(10)+f(5)=55$, what is the value of $a$? A) -5 B) 0 C) 5 D) 10 2. A function $f$ satisfies $f(2)=3$ and $f(3)=5$. A function $g$ satisfies $g(3)=2$ and $g(5)=6$. What is the value of $f(g(3))$? A) 2 B) 3 C) 5 D) 6 3. 4. Answers: C, B, A, D Answer Explanations: 1. As you can see here, we are given our equation as well as two inputs and their combined output. We must use this knowledge to find an element of our output (in this case, the value of $a$.) So let us find our outputs for each input we are given. $f(x) = 5x − 2a$ $f(10) = 5(10) − 2a$ $f(10) = 50 − 2a$ And $f(x) = 5x − 2a$ $f(5) = 5(5) − 2a$ $f(5) = 25 − 2a$ Now, let us set the sum of our two outputs equal to 55 (as was stipulated in the question). $50 − 2a + 25 − 2a = 55$ $75 − 4a = 55$ $−4a = −20$ $a = 5$ Our final answer is C, $a=5$. 2. We're told in the question that $g(3)=2$. To find the value of $f(g(3))$, we need to substitute 2 for $g(3)$. We'll use that value in the $f(x)$ equation. Substituting 2 for $g(3)$ gives us $f(g(3))$ = $f(2)$. We're also told that $f(2)=3$, so that means 3 is the correct answer. Our final answer is B, 3. 3. As per our strategies, we will start by finding the $y$-intercept. We can see in this graph that the $y$-intercept is +2, which means we can eliminate answer choices C and E. (Why did we eliminate answer choice E? Because it had no $y$-intercept, which means that its $y$-intercept would be 0). We can see that the vertex of the graph is at $x=0$ and so it is not shifted to the right or left of the $y$-axis. This means that, in our quadratic equation $ax^2+bx+c$, our $b$ value has to be 0. If it were anything other than 0, our graph would be shifted left or right of the $y$-axis. Now answer choices B and D are squaring expressions, so let us properly FOIL them in order to see the equation properly. Answer choice B gives us: $y=(x+2)^2$ $y=(x+2)(x+2)$ $y=x^2+2x+2x+4$ $y=x^2+4x+4$ This equation would give us a parabola whose $y$-intercept was at +4 and whose vertex was positioned to the left of the $y$-axis (remember, a positive $b$ value shifts the graph to the left.) We can eliminate answer choice B. By the same token, we can also eliminate answer choice D, as it would give us: $y=(x−2)^2$ $y=(x−2)(x−2)$ $y=x^2−4x+4$ Which would give us a graph with a $y$-intercept at +4 and a vertex positioned to the right of the $y$-axis. By process of elimination, we are left with answer choice A. But, for the sake of double-checking, let us test a coordinate point on the graph against the formula. We already know that our equation matches the coordinate points of $(0, 2)$, as that is our $y$-intercept, but there are several more places on the graph that hit at even coordinates. By looking at the graph, we can see that the parabola hits the coordinates $(1, 3)$, so let us test this point by plugging our input (1) into our equation, in hopes that it will match our output of 3. $y=x^2+2$ $y=(1)^2+2$ $y=1+3$ $y=3$ Our equation matches two sets of ordered pairs on the graph. We can reasonably say that this is the correct equation for the graph. Our final solution is A, $y=x^2+2$ 4. Instead of using $x$ for our input, this problem has us use $t.$ If you become very used to using $f(x)$, this may seem disorienting, so you can always rewrite the problem using $x$ in place of $t$. In this case, we will continue to use $t$, just so that we can keep the problem organized on the page. First, let us find the $y$-intercept. The $y$-intercept is the point at which $x=0$, so we can see that we are already given this with the first set of numbers in the table. When $t=0$, $f(t) = −1$ Our $y$-intercept is therefore -1, which means that we can automatically eliminate answer choices B, C, and E. Now let's use our strategy of plugging in numbers again. Our answer choices are between A and D, so let us first test A with the second ordered pair. Our potential equation is: $f(t) = t − 1$ And our ordered pair is: $(1, 1)$ So let us put them together. $f(t) = t − 1$ $f(1) = 1 − 1$ $f(1) = 0$ This is incorrect, as it would mean that our output is 0 when our input is 1, and yet the ordered pair says that our output will be 1 when our input is 1. Answer choice A is incorrect. By process of elimination, let us try answer choice D. Our potential equation is: $f(t) = 2t − 1$ And our ordered pair is again: $(1, 1)$ So let us put them together. $f(1) = 2(1) − 1$ $f(1) = 2 − 1$ $f(1) = 1$ This matches the input and output we are given in our ordered pair. Answer choice D is correct. Our final answer is D, $f(t) = 2t − 1$ You did it! High fives all around. The Take Aways Many students have not dealt a lot with functions, but don't let these kinds of questions intimidate or confuse you when you see them on the SAT. The principles behind functions are a simple matter of input, output, and plugging in values. The test will try to muddy the waters when they can, but always remember that these questions will appear to be more complex than they truly are. Though it can be easy to make a error with your signs or variables, the actual problems are simple at their core. So pay close attention, double-check your work, and you'll soon be able to work through functions problems with little trouble. What's Next? Speaking of quadratic functions, how's your grasp of completing the square? Learn how and when to complete the square with this guide. Phew! Knowing your functions means knowing a significant portion of the SAT math section (round of applause to you!), but there are so many more topics to cover. Take a look at all the topics you'll be tested on in the SAT math section and then mosey on over to our math guides to review any topic you feel rusty on. Not feeling confident about your exponent rules? How about your understanding of polygons? Need to review your slopes? Whatever the topic, we've got you covered! Looking for help with more basic math? Refresh your memory on the distributive property, perfect squares, and how to find the mean of a set of numbers here. Think you need a math tutor? Check out our guides on how to find the tutor that best meets your needs (and your budget). Running out of time on the SAT math section? Not to worry! We have the tools and strategies to help you beat the clock and maximize your point gain. Trying for a perfect score? Check out how to push your score to its maximum potential with our guide to getting an 800 on the SAT math, written by a perfect scorer. Want to improve your SAT score by 160 points? Check out our best-in-class online SAT prep program. We guarantee your money back if you don't improve your SAT score by 160 points or more. Our program is entirely online, and it customizes what you study to your strengths and weaknesses. If you liked this Math strategy guide, you'll love our program. Along with more detailed lessons, you'll get thousands of practice problems organized by individual skills so you learn most effectively. We'll also give you a step-by-step program to follow so you'll never be confused about what to study next. Check out our 5-day free trial:

Terrorism Essay Example | Topics and Well Written Essays - 1000 words - 4

Terrorism - Essay Example ychological concept of chosen trauma is the basis of a section of the society taking retaliatory action against the rest of the society or the part of the society that the group feels has historically oppressed them, without feeling guilty or even considering the adverse effect of their retaliatory actions (Volkan, 2004). This concept is related to terrorism in the sense that; terrorism consists of a group of people in the society who are seeking to attack the rest of the society or at least target the section of the society as a way of avenging for a perceived historical injustice or oppression against them (Volkan, 2004). In this respect, the terrorists engage in attacking and causing harm to the rest of the society without considering that they themselves could be doing something wrong, since chosen trauma makes them feel justified to react to a perceived historical injustice that they feel is unresolved (Volkan, 2004). The sociological aspect of terrorists’ fear of victory refers to the characteristic of terrorism that is different from the rest of violence that are perpetrated in the society. The aspect of terrorists’ fear of victory means that the aim of terrorism is not to perpetrate either terror or violence on their own sake, but with a more unpronounced objective of either instilling fear on the target victims, or to achieve victory through coercing the target victim to fulfill a premeditated intention of the terrorists (Fine, 2008). Terrorism is a form of violence that does not in itself seek to attain personal gains as does with most victims, but to achieve the objectives of a certain section of the society that wants either to make a political statement or instill fear of being a potentially harmful section of the society that is capable of forcing the society to take certain decisions that the society may not be voluntarily open to (Gregg, 2014). Therefore, when terrorists plan an act of terror towards any section of the society, the intention