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Write the domain of each rational expression in set notation

Write the domain of each rational expression in set notation

Explain in your own words what the meaning of domain is. Also, explain why a denominator cannot be zero.
Find the domain for each of your two rational expressions.
Write the domain of each rational expression in set notation (as demonstrated in the example).
Do both of your rational expressions have excluded values in their domains? If yes, explain why they are to be excluded from the domains. If no, explain why no exclusions are necessary.
Incorporate the following five math vocabulary words into your discussion. Use bold font to emphasize the words in your writing. Do not write definitions for the words; use them appropriately in sentences describing your math work.
Domain
Excluded value
Set
Factor
Real numbers

20c3 + 5c2 – c
7c – 14

3a2 – 12a
24a2 – 18a

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  4. 4 Replies to below posts ( ~60 words each) Question 1 Discussion A common theme in late modern North America is the supposed conflict between the rational and the religious—as though the latter is, by definition, somehow non-rational. Where do you see this conflict in The Exorcist? Can you think of other current examples? Q1-1:Rational Religion? Without a doubt, there is an overwhelming push in modern society to understand everything. It seems that the rational conclusion must be true, and the promotion of rational thought will naturally be the end result. Religion is partially involved with the unknown and unknowable. It seems that we live in a world where God cannot be experimentally verified; this devalues traditional rational approaches. In The Exorcist, initially “rational” and scientific explanations are made. Chris first turns to her gods; that is, doctors and psychiatrists. But eventually, their dogmatic insistence on medically explained brain damage (even after it is not medically evidenced) so dramatically fails to correspond to the reality that Chris abandons her conventional “rationality” and turns to a spiritual solution. The Exorcist is a very interesting example of the rational/non-rational dichotomy, as it firmly establishes the nature, source, and reality of the possession. Typical horror/thriller films will overlay spiritual factors but suggest or imply alternate explanations. Films like It, The Ring and It Follows have supernatural forces, but either presents them as alternate lifeforms or leave room for a natural explanation. The Exorcist clearly ties religion to the film; Pazuzu is tied to Babylonian religion and is clearly affected by Christian icons. This implies rational consistency, albeit in a different direction then traditionally taken. Oddly enough, the title is The Exorcist, not The Exorcism, making Father Karras the implied main character, and in him we see doubts about faith ultimately being reconciled with his self-sacrifice. Fundamentally his doubts stem from the rational conflicting with the perceived non-rational and cumulating in a literal leap of faith. Q1-2:Rational vs Religious I would agree that a very common theme in society as of late is the idea that a choice must be made between science and religion… and that those on the religious side are non-rational. A strong example of this in the movie The Exorcist was when Regan’s mom took Regan to go receive medical treatment because she knew something was very wrong with Regan at that time. The doctors spent their time looking for solely “rational” explanations that pertained to the science they had spent years studying and practicing, because that was what was deemed as the only rational explanations to them. The doctors seemed dismissive of things that Regan’s mom was saying and were trying to fit everything that was happening/had happened into their “box of rational”. Part of this was because religion, demons, etc., used to be a lot more widely believed in past centuries. However, in the past few centuries, there has been the increasingly popular idea of being “enlightened” with rational thoughts and science as opposed to religion. This led the doctors to give Regan a diagnosis of a brain disorder because they believed that everything that had been happening had to do with Regan’s brain having issues instead of external factors. Even though Regan’s mom felt there was something else going on that could not be explained in “rational” terms in the opinion of society, the doctors would not entertain such a possibility, because they deemed it non-rational. One very common example of this conflict in North American society are debates of evolution versus creation. These debates tend to be held between a scientist and a religious leader, respectively. The scientists tend to be portrayed as the person making all the “rational” arguments because they seem to be backed up by science and the science community. Then, the religious leader tends to be the one making the more extreme, more out-there arguments. They are portrayed as non-rational, or at least not as rational as the scientist. This has been my experience with these debates in popular culture, at least. Since this is a debate that is relevant in North American society, I believe it is a good example of the rational versus the religious conflict. Question 2 Discussion Supernatural Evil and Religious Fanaticism In The Exorcist, it is clear that the movie depicts the sociophobic fear of supernatural evil through the demonic possession of Regan. But I think the most powerful fear used in the film is that religion will be useless and ineffective at the very moment we need it most; that God will not or cannot save us. This movie spends a great deal of time slowly showing us how all scientific explanations have been thoroughly explored and therefore brings us to possession as the only “logical” conclusion. If this is actually true, to what place other than the church could any of us turn? It becomes our last hope and the chance that it might fail is terrifyingly portrayed in the movie’s dramatic final scenes. While horror is not a genre I have much experience with, I can think of a couple of examples that resonate with me. In The Rite (2011), there is an interesting twist on the fear of supernatural evil, in that it is a priest himself (Father Lucas played by Anthony Hopkins) who becomes possessed. To me this layers in an added element of fear; if even a priest can be possessed, what hope can there be for the rest of us? The Wicker Man (1973), is a great example of the fear of religious fanaticism as it shows “the willingness of people to carry out unspeakable acts in the name of their god” (Cowan, Religion and Cinema Horror, p. 63). It is interesting because not only does the main character have to face the terror of a fanatical cult, but God does not save him! Sgt. Howie is ultimately burned alive due to an irrational belief of the cult that this will save their future crops. There is something very scary about being confronted by a zealot mob with which you cannot reason. This movie also has elements of the fear of the flesh as there are many displays of nudity, public copulation and the sexualization of young girls. This is horrifying to the devout Christian Sgt. Howie. I think the movie is a good example of the anarchy that is the feared (and only?) outcome of religious fanaticism. Sociophobics of ‘Hereditary’ and ‘Midsommar’ One of my favorite horror movies is ‘hereditary’ (2018). The second film I will briefly discuss is more of a physiological thriller, but the element of supernatural evil is present. In hereditary, there are clear sociophobics of death and supernatural evil. One of the main characters dies early in the film in a very uncommon but possible death. She gets beheaded when she sticks her head out of a car window and hits a telephone pole. The randomness of death put me on edge while watching the film because I suddenly became more cautious of my surroundings. This kind of depiction of death in an unusual sense made me more observant and temporarily paranoid about the everyday things I do that could lead to death as uncommon as that one. One interesting thing that the film does in order to raise this fear of ‘supernatural evil’, is to make the protagonist’s efforts pointless. Although several characters in the movie try to fight the entity and prevent more tragedy, supernatural evil prevails and ultimately ends up accomplishing its own goal. This same kind of sociophobic is used in the film ‘Midsommar’ (2019), where the supernatural powers of a cult overpower the protagonist, eventually leading her in to become one of their members. This kind of power shift from the known to the unknown is the root of our supernatural fears. The audience becomes convinced that if this reality the film is depicting is real, that they personally have no power in it. This leads to the question if we are afraid of the unknown or just the unknown being more powerful than we can control?