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Solution: In Exercises 72 to 79, determine whether the graph

College Algebra and Trigonometry | 7th Edition | ISBN: 9781439048603 | Authors: Richard N. Aufmann ISBN: 9781439048603 155

Solution for problem 75 Chapter 2

College Algebra and Trigonometry | 7th Edition

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College Algebra and Trigonometry | 7th Edition | ISBN: 9781439048603 | Authors: Richard N. Aufmann

College Algebra and Trigonometry | 7th Edition

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Problem 75

In Exercises 72 to 79, determine whether the graph of each equation is symmetric with respect to the a. x-axis, b. y-axis, and c. origin

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Chapter Eight Cognition and Intelligence B.F. Skinner believed that language is learned the same way that everything else is learned, through imitation, reinforcement, and other types of conditioning. This is the behaviorist theory. He said that if vocalizations are not reinforced they will start to gradually decrease. Noam Chomsky thought that since there are so many words in a language, it would be impossible for language to be learned through imitation. He said that children learn the rules of language. He believed that humans have an inborn propensity to develop language. This is the nativist theory. It involves the language acquisition device (LAD). It is a mechanism that facilitates the learning of language. The exact nature of this has not been figured out-­‐ just that humans have brain structures that make us equipped for learning language. He believed this because he saw how it was so easy for children to learn language. There were some people who questioned Chomsky as well, because they wanted to know more of what structures were involved in the LAD. These people believe that it wasn’t accurate to compare how well a toddler can learn a language since they’re more involved with it, as opposed to a teenager learning a foreign language in high school. Another theory, the interactionist theory, said that it was a combination of biology and experience that shape language. They believe that there are brain structures equipped for this learning and that children follow rules of language, but also that interactions with parents influence the learning of language. Bilingualism is being able to speak two languages that use different speech sounds, vocabulary, and grammatical rules. Many people believe that bilingualism hampers language development and has a negative impact on the education process. Studies have shown that bilingual children have less vocabulary in each of their different languages than monolingual children have in their language, but that when the languages are put together they have more vocabulary. Bilingual and monolingual children are similar in their rate of language development. Some disadvantages of bilingualism are that the processing speed of words is slightly slower and the ability to think of words they want to use is also slower. Bilingual individuals have been found to score higher on tests for attention control and other types of problem solving tests. Benjamin Whorf was the most prominent supporter of linguistic relativity. This is the hypothesis that one’s language determines that nature of their thought. He said that people of different language have different views of the world. The English language only really has one word for snow, while other languages have more than one word. Some languages group some colors together into one color such as blue and green. These people might think of these colors differently than people of the English language do because we have one color for each of them. In problem solving, you must go beyond the normal amount of thinking required for a normal level question. If advanced thinking were not required, then it wouldn’t be a problem. There are 3 types of problems associated with problem solving. The first one is problems of inducing structure. This is when you have to solve analogy or series completion problems. You are discovering relationships between the parts of the problem. Another type is problems of arrangement. This is when you have to put the parts of the problem together in some way to satisfy a goal. There will only be one way to find the solution. The last type is problems of transformation. This is when you have to carry out a sequence of different things in order to get to a goal. These can be really challenging. There are also some barriers to problem solving. The first barrier is irrelevant information. This is when too much information is given in the problem that is not needed to solve the problem. This can be a distraction and make it harder to solve the problem. Usually whenever numbers are present in a problem people assume that it is needed to solve the problem. Another barrier is functional fixedness. This is when you think about an object in only the way that it is supposed to be used. This is an issue because people tend to overlook the small features of objects. Another barrier is mental set. This is when someone is set on using a problem solving method that worked for him or her in the past. Sometimes this means that you will be trying to do too much work for a simple problem. The last barrier is unnecessary constraints. This is when you think there is a certain constraint to a problem when there actually isn’t. This requires you to think outside of the box. Insight is when someone finally comes to the realization of what they have to do to solve the problem after they have been struggling with it for a while. There are different approaches used when trying to solve problems. Trial and error is a very common method. This is when many different possibilities of solutions are tried, and the ones that don’t work are removed from consideration. This can be effective when there are only a few methods to choose from. This is not effective when there are many possible solutions. A heuristic is basically a “rule of thumb” used when solving problems. Forming subgoals is another approach to solving problems. Subgoals are intermediate steps involved in solving the problem. Reaching subgoals means you are closer to solving the problem. Another method to solving problems is searching for analogies. This is just when you recognize the similarity between parts of the problem. Changing the representation of the problem is another approach to solving problems. Using lists, tables, or graphs work better for some people than others. Putting the problem into a representation that works the best for you is a good approach to solving the problem. Taking a break from the problem when you cannot find a solution can be helpful when trying to solve a problem. After taking a break and coming back you may find that you see the problem in a different light. The incubation effect is when new solutions come up after there was period of not thinking about the problem. Risky decision-­‐making is when you have to make a choice that you have some uncertainties about. This is when you don’t know the outcome of your decision. Availability heuristic is when an estimated probability is based on the number of instances that come to your mind. This can cause the probabilities to not be accurate. Representativeness heuristic is when the estimated probability is based off of the typical prototype of the event. This would be like estimating the probability of the number of tails flipped in 6 trials based off of the fact that a typical event of this would have only half of the trials being tails. The tendency to ignore base rates is when you base your decision on the characteristics rather than the base rate. You ignore the relative amounts of each different type of person in the world. Example from book (page 275): just because the characteristics were of a librarian it is still more likely that Steve is a salesperson because the number of salespeople outnumber the number of librarians by a lot. The conjunction fallacy is when people think that the odds of two events happening together is greater than the odds of either or them happening alone. These are both influenced greatly by representativeness heuristic. Some people have said that human thinking is not very rational or effective, but others believe that it only seems this way because problems are being asked and formed in the wrong ways. The questions are not asked in a way that the human mind has been evolved to solve. The fast and frugal heuristic is that all organisms have to be able to make decisions under very demanding circumstances. In other words, organisms do not have the time, resources, or all of the relevant information needed to form a proper decision. An expansion of this is the recognition heuristic. This is the fact that if two options are given and only one of them is recognized, that will most likely be chosen. Reliability refers to measurement of consistency of a psychological test. This means that there are similar scores for each repetition of the test. This helps correct correlation coefficients to be found, which are used to determine how much two variables are related, if at all. IQ tests do yield reliable results. Validity is the ability of a test to be able to measure what it was intended to measure. IQ tests are valid, but only if you are referring to academic work. If you were referring to intelligence in a broader sense, then they would not be quite as valid. There are some people who had major contributions to the subject of intelligence. Alfred Binet and Theodore Simon created the first useful test for general mental ability. It was inexpensive, easy to give to students, and very good at predicting children’s mental capability. This scale expressed the child’s score in terms of mental age. It gave the age that the child’s mental ability was displaying from the test. Lewis Terman did some revisions to Binet’s test after he died. It used a new scoring technique, the IQ. This is the child’s mental age, divided by chronological age, multiplied by 100. He was the person behind schools adopting the IQ test. It is still the most widely used psychological test. David Wechsler came up with the first IQ test for adults (Wechsler Adult Intelligence Scale-­‐ WAIS). He used a test that was not as dependent on verbal ability. A lot of the items on the test were about nonverbal reasoning; others were still about verbal reasoning. He gave separate scores for each of these, and then totaled them up. This has been adopted by all of the other IQ tests. IQ scores are distributed on a normal curve with a mean of 100 and a standard deviation of 15. 68% of people fall within one standard deviation of the mean, 96% of people fall within two standard deviations of the mean, and 99% of people fall within three standard deviations of the mean. This allows us to be able to classify the intelligence of someone based on how they compare to other people on a normal curve. IQ tests are able to measure the mental ability needed for academic success. They are not able to measure anything about social competence, problem solving skills, creativity, or artistic talent. Heredity has a contribution to intelligence. Twin studies are used to determine the role of genetic factors in intelligence. Fraternal and identical twins usually grow up in the same environment, but only identical twins have no difference genetically. So, if identical twins are more similar to each other by intelligence than fraternal twins are to each other, it is most likely because they have a greater genetic similarity. Results from some of these tests show that intelligence is inherited to a considerable degree. Adoption studies can also be used to determine the role on genetic factors in intelligence. If adopted children have more of an intelligence similarity to their biological parents than they do to their adoptive parents, it supports the hypothesis that genetic factors influence intelligence. A heritability ratio is used to estimate the proportion of trait variability in a population that is determined by any differences in genetic inheritance. There are some limitations to these because they can only be applied to groups, not individuals. The heritability of a trait is also able to change during a lifespan. It has been shown that it increases with age. The heritability for specific traits can vary between different groups of people because of different factors. Environment also has a lot of influence of intelligence. Adoption studies can be used to show this because adopted children do show some similarity to their adoptive parent’s in their IQ. Even children that were raised together in the same home but are unrelated have similar IQs. Living in a deprived or an enriched environment can influence one’s intelligence. Researchers studied how children who went from a deprived environment and placed into an environment better suited for learning had higher IQs than siblings who did not make it to a more enriched environment. The Flynn effect shows how IQ tests have increased over generations. Most people agree that this has to be due to environmental effects because the gene pool could not have just changed overnight. Heredity and the environment both influence intelligence. Some people believe that heredity gives limits to intelligence and the environment is what determines where people fall within these limits. This means that there is a “maximum level” to someone’s IQ that cannot be passed even by having outstanding environmental conditions. Extreme circumstances would be able to knock a person below the “minimum level”, though. The reaction range model says that children who have a high-­‐quality environment should be at the very top of their IQ range. Children who have a low-­‐quality environment should be more towards the bottom of their IQ range. The average IQ for minority groups in the United States is lower than it is for whites. Data has shown that the difference between them has decreased over the recent decades. A lot of controversy was sparked over different reports that were published stating how this was due to hereditary differences, and how these were a result of ethnicity. Another explanation was the socioeconomic disadvantage. The gist of this explanation is that minorities tend to grow up with more of a disadvantage, as opposed to whites that have more of an advantage. This could be the cause of lower IQ scores in minorities compared to whites. Researchers feel like we need to expand the measure of intelligence to include things other than just “school smarts”. Higher IQ has been linked to having a longer life. This could be because good genes are both for high IQ and good health. Another explanation is that self-­‐care is something that people with higher IQs are better at. Another explanation is that higher IQs led to a higher socioeconomic class, and most likely a less stressful job, which in turn allows people to live longer. Robert Sternberg said that there are three factors of intelligence. He said that they were practical, analytical, and creative intelligence. Practical intelligence is the ability to be able to deal with everyday life problems. Analytical intelligence is the ability to reason, evaluate, and give judgment. This is the kind of intelligence needed for school things. Creative intelligence is being able to create new ideas and deal with novel problems. Howard Gardner tried to expand intelligence into nonacademic areas. He did this by looking at the mental capacities of normal people, people who had brain damage, and people from certain populations, such as idiot savants. He said the 8 types of intelligence were: • Logical-­‐mathematical • Linguistic • Musical • Spatial • Bodily-­‐kinesthetic • Interpersonal • Intrapersonal • Naturalist Personal Application-­‐ Measuring and Understanding Creativity • Creativity is the generation of original ideas that are useful. • In convergent thinking one tries to narrow down a list of options to get to the correct answer. • In divergent thinking one tries to expand the amount of options. • There are creativity tests that are given that have a bunch of questions that involve one being creative. • There is not a single personality for creativity. • There is not a strong correlation for high IQ and high creativity, but there is for mental disorders and high creativity. Some information found from: Weiten, Wayne. Psychology: Themes and Variations. Boston: Cengage Learning, 2014. Print.

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Textbook: College Algebra and Trigonometry
Edition: 7
Author: Richard N. Aufmann
ISBN: 9781439048603

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Solution: In Exercises 72 to 79, determine whether the graph