Are You Distracted by Technology essayEssay Writing Service

Are You Distracted by Technology essayEssay Writing Service Are You Distracted by Technology? essay Are You Distracted by Technology? essayNowadays technology entered all spheres of human life and contributed to significant changes in these spheres. Communications were dramatically reshaped by technology: the availability of social networks, video games and various smartphone and computer applications allows to stay connected 24/7 and to construct own virtual world in the most convenient way. Despite numerous advantages, active use of technology also has some notable disadvantages such as excess flow of information and frequent distractions damaging the ability to concentrate. Multitasking which is so common for all technology-related activities also alters the ability to focus on particular tasks and reinforces patterns of brain activity which are different from less technology-involved generations. The purpose of this paper is to discuss the distracting impact of technology and long-term consequences of this impact.The role of technology in educational sphere and in information p rocessing is invaluable; for example, technology changed the way of conducting research for students, made research findings more accessible and comprehensive for students and eased access to information in general. At the same time, mental habits of multitasking and staying online in social networks and messengers have a negative impact on the ability of students to process information, to concentrate on particular sources and to establish analytical connections between different sources of information. According to Prakash (2012), 87% of teachers note that students of the wired generation have shorter attention spans and 64% of teachers admit that technology is rather distracting students than helping their academic success.The way how information is presented and shared nowadays encourages people to focus on key concepts and sentences and skim the meaning of the messages. These skills are needed in order to navigate through multiple sources of information and multiple messages re ceived from these sources. Communications in social networks and messengers are also brief and are restrained either to sharing some information (links, photos, videos, etc.) or to exchanging short messages. Twitter actually embodies the essence of current communications 140 symbols might be enough for average information exchange activities. Furthermore, the availability of internet connection almost anywhere allows to stay online and receive updates at any time.The specifics of technology described above leads to shortening of attention spans; frequent checks of updates in various networks create distractions, and the need to stay updated and to know all the latest news hinders long-term concentration and affects the quality of activities which require thoughtful approach. Furthermore, kids who grow up in the conditions of information overload have difficulties in mastering time management and attention management. While for older adults who already have mastered time management it is easier to avoid distractions when needed, kids might not be able to develop the right skills and traits due to challenging environment.According to Rosen (2012), observation of the ability to concentrate of students of various age (middle school, high school and university) revealed alarming trends. The students had to study something important for 15 minutes, and their behaviors and distractions were observed during that time. The average time span that students spent on the task without distracting was 3 minutes (Rosen n.d.). This result was similar for all age categories of students. The major sources of distraction were technology sources such as laptops and smartphones (Rosen n.d.). These results show that the impact of technology is similar on all age categories. Furthermore, the researchers explored the relationship between academic performance and distractions, and it turned out that students who consumed more information and media every day and were prone to multitask ing had worse results. Students who were able to work longer on a specific task and developed focused study strategies showed better results (Rosen n.d.).Another study focused on the types of distractions which have the most impact on young people. It appeared that the choice of favorite distraction depended on psychosocial characteristics of an individual (Richtel n.d.). The students with a need for socializing tended to engage in texting, communicating in social networks and sending instant messages; the students who wanted to escape from the society chose video games and those students who had a tendency to procrastinate surfed various websites, watched videos and sometimes shared links with others (Richtel n.d.). Therefore, technology allows to choose the types of distractions that are most appropriate for an individual. In any case, the results of the research show that technology is a universal distraction and that active use of technology for entertainment can affect academic or working performance.Evidence shows that technology is a powerful distraction for most people. Active use of telecommunications leads to multitasking, reduces performance and attentiveness, affects attention spans and the ability to concentrate. While working with multiple sources of information might develop flexibility and short-term involvement, it is necessary to avoid excess multitasking and being distracted by technology since it can reduce the efficiency of in-depth thinking activities. In this context, it is important to remain focused in the modern world and to train the ability to concentrate on important things instead of switching between various distractions.

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:

Management environment and leadership Assignment

Management environment and leadership - Assignment Example ty in capital-intensive industries, an unstable oil cartel, raiders with junk bonds, and the changing demographics of the work-force are among the many factors that have contributed to this shift.   The net result is that doing what was done yesterday, or doing it 5% better, is no longer a formula for success. Major changes are more and more necessary to survive and compete effectively in this new environment. More change always demands more leadership. Motivational and inspirational quotes, poems, posters, motivational speakers and stories, team building and activities, all develop employee motivation for sales and business staff in all kinds of organizations. Motivational and inspirational experiences improve employees attitudes, confidence and performance. Good leadership demands good people-motivation skills and the use of inspirational techniques. Motivational methods are wide-ranging, from inspirational quotes and poems, to team building games and activities, as ice-breakers, warm-ups and exercises for conferences, workshops, meetings and events, which in themselves can often be helpful for staff motivation too. People playing games or competing in teams learn about each other, they communicate better and see each other in a new light. Mutual respect grows. People often enjoy events which include new non-work activities, especially when bosses and superiors take part in the same teams as their junior staff, which also helps cohesiveness and can-do culture. Inspirational quotes, stories and poems all help motivation too. Powerful positive imagery stimulates visualization in the conscious and sub-conscious brain, which encourages self-motivation, developmental behavior, confidence and belief. Playing games enables people to experienc e winning and achieving in a way that their normal work might not. People become motivated to achieve and do better when they have experienced the feelings of success and achievement, regardless of context. This is why

Management environment and leadership Assignment

Management environment and leadership - Assignment Example ty in capital-intensive industries, an unstable oil cartel, raiders with junk bonds, and the changing demographics of the work-force are among the many factors that have contributed to this shift.   The net result is that doing what was done yesterday, or doing it 5% better, is no longer a formula for success. Major changes are more and more necessary to survive and compete effectively in this new environment. More change always demands more leadership. Motivational and inspirational quotes, poems, posters, motivational speakers and stories, team building and activities, all develop employee motivation for sales and business staff in all kinds of organizations. Motivational and inspirational experiences improve employees attitudes, confidence and performance. Good leadership demands good people-motivation skills and the use of inspirational techniques. Motivational methods are wide-ranging, from inspirational quotes and poems, to team building games and activities, as ice-breakers, warm-ups and exercises for conferences, workshops, meetings and events, which in themselves can often be helpful for staff motivation too. People playing games or competing in teams learn about each other, they communicate better and see each other in a new light. Mutual respect grows. People often enjoy events which include new non-work activities, especially when bosses and superiors take part in the same teams as their junior staff, which also helps cohesiveness and can-do culture. Inspirational quotes, stories and poems all help motivation too. Powerful positive imagery stimulates visualization in the conscious and sub-conscious brain, which encourages self-motivation, developmental behavior, confidence and belief. Playing games enables people to experienc e winning and achieving in a way that their normal work might not. People become motivated to achieve and do better when they have experienced the feelings of success and achievement, regardless of context. This is why

Management environment and leadership Assignment

Management environment and leadership - Assignment Example ty in capital-intensive industries, an unstable oil cartel, raiders with junk bonds, and the changing demographics of the work-force are among the many factors that have contributed to this shift.   The net result is that doing what was done yesterday, or doing it 5% better, is no longer a formula for success. Major changes are more and more necessary to survive and compete effectively in this new environment. More change always demands more leadership. Motivational and inspirational quotes, poems, posters, motivational speakers and stories, team building and activities, all develop employee motivation for sales and business staff in all kinds of organizations. Motivational and inspirational experiences improve employees attitudes, confidence and performance. Good leadership demands good people-motivation skills and the use of inspirational techniques. Motivational methods are wide-ranging, from inspirational quotes and poems, to team building games and activities, as ice-breakers, warm-ups and exercises for conferences, workshops, meetings and events, which in themselves can often be helpful for staff motivation too. People playing games or competing in teams learn about each other, they communicate better and see each other in a new light. Mutual respect grows. People often enjoy events which include new non-work activities, especially when bosses and superiors take part in the same teams as their junior staff, which also helps cohesiveness and can-do culture. Inspirational quotes, stories and poems all help motivation too. Powerful positive imagery stimulates visualization in the conscious and sub-conscious brain, which encourages self-motivation, developmental behavior, confidence and belief. Playing games enables people to experienc e winning and achieving in a way that their normal work might not. People become motivated to achieve and do better when they have experienced the feelings of success and achievement, regardless of context. This is why

Arts education interpretation activity Essay Example | Topics and Well Written Essays - 4000 words

Arts education interpretation activity - Essay Example ging from English proficiency to mathematics, however this fails to address the psychological and sociological problems that often serve as the catalyst for re-offending. In order to get to the root of what actually drives prisoner desire to continue a life of criminal behaviour, there needs to be more focus on establishing relationships with habitual offenders to alter these behaviours that pose risk and danger to the whole of society. This serves as the appropriate rationale for the development and launch of an arts education program. Art education, at is foundations, delivers on social justice by promoting social inclusion, establishing emotional intelligence for cultural diversity, and also promotes a desire within arts-educated individuals to continue pursuing life-long learning. Why is this? Arts education inspires a sense of social inclusion for those in the prison system who currently feel alienated and shunned from the rest of society (Kotler Trust 2013). Prisoners can be taught the fundamentals of higher education routinely, which would certainly build their competencies in mastering knowledge. However, only arts education maintains the potential to alter social attitudes and create important psychological connections between culture and the self, thereby inspiring an individual within the prison system to explore maximising their own potential. This proposed arts education pack is designed to build psych o-social strengths within conflicted and frustrated prison populations for long-term rehabilitative outcomes and removing risks from society from those prisoners unable to find appropriate cultural connections that motivate compliance with the social order. The term arts can be interpreted in many ways, including tangible renditions of sculpture, paintings, and music. For this arts education program, however, the intangibles of arts as it pertains to cultural awareness and cultural inclusion make up the foundation of how this education program will be

Modern British Cinema: Themes and Perspectives

Modern British Cinema: Themes and Perspectives INTRODUCTION The history and rich heritage of the modern British cinema can be rooted from its rich history and films which were produced in the past and served as an unwavering inspiration to the themes and perspectives which were evident in the British films which were shown today. One of the most common themes existent among the British films of today would most probably be the concept of social realism. This theme, as being present and influential in the production of modern British films, represents the actual happenings in the real lives of the people, together with all the difficulties and predicaments which were present in the peoples daily struggle to survival. The stories and the people which were portrayed in the films were reflective of everyday characters and usually are have an economic background belonging to the middle class group in the society. The theme of social realism started to be portrayed in British films in as early as the 1960s with also the emergence of the so-called B ritish New Wave. Some of the films in the past which showed themes of social realism include Look Back in Anger, Saturday Night and Sunday Morning, and The Loneliness of the Long Distance Runner. Because of the presence of social realism in various literatures in the past, most of these movies were based on written novels and produced plays which showed the same theme. Furthermore, it has been noted that social realism is more than just a genre in modern British cinema, it is considered to be a dominant form of cinema. This theme of social realism is often coupled with political awareness as such has been also noted to be permissive in British cinema. Modern films with the themes of social realism include Trainspotting, My Name is Joe, This is England, and Human Traffic (Strozykowski, 2008) Moreover, new perspectives in the British cinema is also said to have been focused in masculinity, showing themes which were centered and aptly inspired by the British men in the society, or at least, the crisis in British masculinity. Furthermore, more than the crisis, it is said that what the British cinema actually articulates would be the dilemmas of identification and ideology for modern British men. (Claydon, n.d.) LOOKING FOR ERIC One of the British films in the modern society would have been Looking for Eric which was show in theaters last year. The central theme which was depicted in the movie Looking for Eric could be aptly described as how a football player was able to run away from the trials and problems which life has confronted him and it also shows how the heroes of footballs can bring for fans. The movie was directed by an English director in the name of Ken Loach while the story was written by Paul Laverty. The main casts of the movie included real-life football fantasy and superstar, Eric Cantona together with Steve Evets. According to the director of the film, the movie was actually intended to show the life of major celebrities as being only as simple and as complicated as everyone life and the notion that we are stringer as a tem rather than as separate individuals with differing goals and perspectives. The film was also used as an entry in a competition, the 62nd Cannes Film Festival. The movie was considered to be an exceptional addition to the glitz and glamour of the film festival as it showcased the presence of the Manchester United and France footballing legend. The film was shot in the United Kingdom, distributed by Icon Film Distribution and produced by the company owned by Loach which was Sixteen Films. It was said to have an estimated budget of 4 million pounds. THE SYNOPSIS AND PLOT The movie depicts a bitter sweet comedy illustrating the life of a loser postman who was able to receive words of wisdom from Eric Cantona, who is also Eric Cantona in real life, a philosophical football legend who is considered to be the hero of another character in the said movie. The movie is also said to be a significant addition to the list of movies which were football related in terms of the story or the central plot. The movie was all about a middle-aged postman who was able to find employment at the Manchester sorting office through the character of Eric Bishop. Bishop in the movie was going through a dreadful crisis in life which sprouts other themes which were evident through the course of the film. Bishop was alo looking through and guiding the growth of his grand daughter which makes him make contact with his ex-wife, Lily. The grand daughter is a main reason why he needed to still establish close relationship and contact with Lily despite the fact that the two were already separated after Bishop abandoned her when their first child was born. His son, Ryan, was then hiding a gun in their house which is used by the gangsters which are present in the place. In one of Bishops weakest and most depressing time, he considers the possibility of committing suicide in order to end the adversaries which have been confronting his life. Furthermore, in order to discount the possibility of such occurrenc e, a meditation session was held inside his room and after which, he had a clearer perspective of things and let go of the possibility of ending his only life and instead went to see the philosophical football legend which happens to be another Eric, in the person of Eric Cantona. His visits to the football star were able to give him enlightenment after Cantona gave him several words of wisdom and inspiration which gave him ideas on why he should go on with his life. Such visits led to an improvement in his relationship with his ex-wife. Bishop also discovered about the hidden gun and he immediately confronted his son after finding it out. When his son was confronted, Ryan did not deny of his involvement with the gangsters in the place. Bishop returned to the gun the rightful group. His sons were said to be making his life more problematic and they are deemed to bring Bishop into an early death with all the problems that the two have caused in Bishops life. When he returned the gun, he was forced to keep it himself and a series of unfortunate events followed which even included a posting of a humiliating video of him in a video uploading site. The entire family was then arrested and the house was searched in order to find the gun but it was nowhere to be found all over the place. Bishop was given different words of wisdom and advice by Cantona. With a number of fanatics of the Manchester United football team, in an operation which they dubbed as Operation Cantona, Bishop sneaked through the gangsters house to be able to find the gun and threatened that they will also release a humiliating video of the gang just like what they have earlier did to Bishop. Cantona was considered by Bishop to be like a genie who suddenly pops out of the bottle, acted his life coach, and gave him more inspiration and reasons to be able to enjoy and live life despite the predicaments especially with all the trouble that confronted him as being brought about by his children. The movi e ended with the scene of a graduation of one of Bishops children, depicting a happy family and finally enjoying a peaceful life. CLOSER LOOK AT THE MOVIE With the central characters which assumed the major roles in the movie, it can be said that the film revolved around the lives of two Erics Bishop and Cantona who each had their fair share in the flow of the story. The first Eric is the depressed one who has been confronted with numerous challenges in his life, from his children, to his ex-wife, and even to the environment in which he has been living. However, the second Eric was legendary and ghost-like. He was like a genie who provided words of wisom and encouragement to be able to inspire the former Eric in his life amidst all the struggles which confronted him. Like in any other works of Ken Loach, the movie included a spectacular cast which has been deemed to be perfect in the portrayal of their respective roles in the movie. The meticulous casting process for Looking for Eric is said to be an additional in the bones of the character and also serves as an embellishment in the whole process of completing the movie. In the movie, the most important and central character is not the legendary football player, but the little Eric who found inspiration in the middle of his struggle to survival. Moreover, the humor in the story can be especially seen and illustrated in the scenes where Cantona has been giving the other Eric a series of advises to help him go on with living his life instead of trying to end it because he was confronted with too many troubles. Form this advises, there were presence of self-deprecating humor which included his metaphors. The enigmatic philosophical ramblings of Cantona were depicted in the film without losing the to uch of humor to provide more interest in the storyline (Strozykowski, 2009). The presence of social realism in the central theme of the film cannot be also discounted as the main characters and setting of the film revolves around the middle class society and reflects their struggle for survival in the middle of the illustrated political and economic situation. THE DIRECTOR As what has been mentioned earlier, the movie was directed by Kenneth â€Å"Ken† Loach, a native of Warkwirshire. His earliest experiences in the fields of movie and television can be attributed to his membership at his schools experimental theater club. His first experiences in directing were harnessed as he joined ABC television in the year 1961and he then switched to BBC after several years. One of his most notable works in the field of television entertainment would have been The Wednesday Play which he did in collaboration with the skills of Tony Garnett. The said work of the two directors is said to have been a significant evolution and revolution in the field of British drama as such show has spurred political debates. The drama is said to be a socialist as it has been geared towards providing an inspiration to the middle class members of the society to become agents who could be able to potentially revolutionize and inspire the existence of economic change in the Briti sh society. Ken Loach has always been a name surfacing in the Cannes Film Festival as his works have made him one of the favorites in the said award-giving body. During the eyar 2006, the director won the most prestigious award at Cannes, the Palm dOr for his movie entitled The Wind That Shakes the Barley which is about the troubles in Ireland. The most successful works of Loach in the field of British entertainment were said to be exploratory of the varying dimensions of the life of human wherein the personal dimensions intersect with the political aspects. His works show the fusion of politics with the lives of ordinary human beings and how such can greatly affect the mode of living. Much of the directors works were aimed towards the criticism of capital targets which included gangsters, exploitative employers, conservative employers, and loan sharks, which have been a common theme in his works. The artistic visual style of Loach as a director is said to be unassuming, illustrating careful narrative construction, and showing performances which are sympathetic making the target audience relate into the situations which were depicted by the motion picture. The political points which Loach tries to emphasize in his works could be seen arising from natural emotions and situations which are shown to be very realistic. The exis tence of humor in his works cannot be also discounted as such themes make the claims of the film stronger, and at times, can also add sarcasm to the political satires which the film expects to deliver. Loach has already an experience of almost 40 years in the industry with an estimated works of almost 60 films which included theatrical figures and works which were intended not to be show in cinemas but only in the televisions yet still depictive of the same themes and concepts which were common in the directors works. It has been said that most of his finest works were explicitly political with a tough of humor and powerful emotion inspired by the directors intellectual ideas and major concepts. His works were said to be one way of depicting the nations unconscious as it illustrates what has been actually happening in the modern society in terms of the political and economic dimension. Despite hindrances in the industry such as financial constraints, fickle artistic trends, and the ebb and flow in politics, Loach remains in his commitment of providing the society with films which are committed to progressive ideals. The most powerful scene sin the movies which were created by Loach were said to be established in a setting were a large group of film characters were gathered as they discuss and debate over various issues, mostly were political and economical. For instance, in his movie The Big Flame the characters were shown to be having a conversation as they try to organize a strike, in the movie Land Of Freedom there was also a scene which depicts an extended debate in which the characters were fighting about land reform, and the movie Bread and Roses depicted a scene where the janitors were having an argument on whether or not they will be joining an established union. Other works of Ken Loach include the following movies: Poor Cow, Kes, family Life, Black Jack, Looks and Smiles, Fatherland, Hidden Agenda, RiffRaff, Raining Stones, Ladybird Ladybird, Land and Freedom, Carlas Song, My name is Joe, Bread and Roses, The Navigators, Sweet Sixteen, Ae Fond Kiss, Tickets, McLibel,.The Wind That Shak es the Barley, Its a Free World, and Looking For Eric (Robins, n.d.). REFERENCES: Strozykowski, M; Social Realism in British Film; 2008 Claydon, A. E.; New Perspectives on British Cinema: Going Beyond the Crisis in Masculinity Robins, M; Senses of Cinema: Ken Loach The Internet Movie Database; Looking for Eric; 2009 The Official Website of Looking for Eric The Movie; 2009