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Cấu trúc

  • Domain and Range

  • Finding the Domain of a Function Defined by an Equation

  • Using Notations to Specify Domain and Range

  • Finding Domain and Range from Graphs

  • Finding Domains and Ranges of the Toolkit Functions

  • Graphing Piecewise-Defined Functions

  • Key Concepts

  • Section Exercises

    • Verbal

    • Algebraic

    • Graphical

    • Numeric

    • Technology

    • Extension

    • Real-World Applications

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Tài liệu PDF Domain and Range tài liệu, giáo án, bài giảng , luận văn, luận án, đồ án, bài tập lớn về tất cả các lĩnh vự...

6.3 Use Wildcards and Ranges of Values in a SQL Query I need to be able to either search for a range of values, or at least be able to use wild cards with my query. How do I do this using T-SQL? Technique This is one of those fairly simple but necessary How-Tos. You will learn how to use a combination of both wild cards and a range of values. Here is the T-SQL routine that you will use for this How-To: SELECT Customers.CompanyName, Orders.OrderID, Orders.OrderDate FROM Orders INNER JOIN Customers ON Orders.CustomerID = Customers.CustomerID WHERE Customers.CustomerID LIKE 'A%' AND Orders.OrderDate BETWEEN '11/01/1996' AND '12/01/1996' Note The literal values have been used here, rather than the text box values that will be used in the How-To. Using Wild Cards Fairly similar to the wild cards of the old DOS days, wild cards in T-SQL are fairly straightforward to use. It is just a matter of knowing which one to use for which task. When using wild cards, you will use the LIKE operator, as seen in the SQL string for this How-To. You can see where the LIKE operator is used with A%. The % is used to specify anything after the given letter. In this case, it's used for anything starting with the letter A. (This operator will, of course, have to have the OrderDate fall between the dates specified, but we'll talk about this in a moment. You can use other wild cards as well, such as the following: • % (Percent sign). You use this to specify any given group of characters. If used before a letter or group of letters, you are then specifying that you want values ending with those letters. For instance, if you specify %ing, you get skiing, flying, and so on. • _ (Underscore). You use this to specify a single character. For instance, if you type _ake, then you would get four-letters words, such as lake, bake, and sake. • [] (Square brackets) This is a range or group of characters to compare against. For example, if you type [B-D]ake, you would get bake and cake. Another way to use it, with a group of letters, would be to type [BF]ake. In this case, you would get bake and fake, but not the other letter that fall inbetween. • [^] (Caret). This is not within the given range or group. Opposite of the last entry, if you typed [^B-D]ake, you would get those words ending in ake, where the first letter doesn't fall within B-D. The same works for the group of letters as well. Using BETWEEN When you need to look at a range of values, whether it be numbers or dates, you use the BETWEEN operator. The syntax for BETWEEN is as follows: table.column BETWEEN startingvalue AND endingvalue This returns all records where the given column falls between the two values, including the two values. Because the BETWEEN statement mentioned a moment ago was Orders.OrderDate BETWEEN '11/01/1996' AND '12/01/1996', then those records with the OrderDate falling between 11/1/1996 and 12/1/1996 inclusively will be displayed. Steps Open and run the Visual Basic .NET-Chapter 6 solution. From the main form, click on the button with the caption How-To 6.3. When the form loads, you will see a form that allows you to specify letter(s) for the company name to fill the data grid for, along with a range to specify for order dates (see Figure 6.4). 1. Create a Windows Form. Then place the controls listed in Table 6.3 with the following properties set, as displayed in Figure 6.4. Table 6.3. Control Property Settings for This Domain and Range Domain and Range By: OpenStaxCollege If you’re in the mood for a scary movie, you may want to check out one of the five most popular horror movies of all time—I am Legend, Hannibal, The Ring, The Grudge, and The Conjuring [link] shows the amount, in dollars, each of those movies grossed when they were released as well as the ticket sales for horror movies in general by year Notice that we can use the data to create a function of the amount each movie earned or the total ticket sales for all horror movies by year In creating various functions using the data, we can identify different independent and dependent variables, and we can analyze the data and the functions to determine the domain and range In this section, we will investigate methods for determining the domain and range of functions such as these Based on data compiled by www.the-numbers.com The Numbers: Where Data and the Movie Business Meet “Box Office History for Horror Movies.” http://www.the-numbers.com/market/genre/Horror Accessed 3/24/2014 1/46 Domain and Range Finding the Domain of a Function Defined by an Equation In Functions and Function Notation, we were introduced to the concepts of domain and range In this section, we will practice determining domains and ranges for specific functions Keep in mind that, in determining domains and ranges, we need to consider what is physically possible or meaningful in real-world examples, such as tickets sales and year in the horror movie example above We also need to consider what is mathematically permitted For example, we cannot include any input value that leads us to take an even root of a negative number if the domain and range consist of real numbers Or in a function expressed as a formula, we cannot include any input value in the domain that would lead us to divide by We can visualize the domain as a “holding area” that contains “raw materials” for a “function machine” and the range as another “holding area” for the machine’s products See [link] We can write the domain and range in interval notation, which uses values within brackets to describe a set of numbers In interval notation, we use a square bracket [ when the set includes the endpoint and a parenthesis ( to indicate that the endpoint is either not included or the interval is unbounded For example, if a person has $100 to spend, he or she would need to express the interval that is more than and less than or equal to 100 and write (0, 100] We will discuss interval notation in greater detail later Let’s turn our attention to finding the domain of a function whose equation is provided Oftentimes, finding the domain of such functions involves remembering three different forms First, if the function has no denominator or an even root, consider whether the domain could be all real numbers Second, if there is a denominator in the function’s equation, exclude values in the domain that force the denominator to be zero Third, if there is an even root, consider excluding values that would make the radicand negative Before we begin, let us review the conventions of interval notation: • The smallest term from the interval is written first 2/46 Domain and Range • The largest term in the interval is written second, following a comma • Parentheses, ( or ), are used to signify that an endpoint is not included, called exclusive • Brackets, [ or ], are used to indicate that an endpoint is included, called inclusive See [link] for a summary of interval notation 3/46 Domain and Range 4/46 Domain and Range Finding the Domain of a Function as a Set of Ordered Pairs Find the domain of {(2, 10), (3, 10), (4, 20), (5, 30), (6, 40)} the following function: First identify the input values The input value is the first coordinate in an ordered pair There are no restrictions, as the ordered pairs are simply listed The domain is the set of the first coordinates of the ordered pairs {2, 3, 4, 5, 6} Try It Find the domain of the function: {(−5, 4), (0, 0), (5, −4), (10, −8), (15, −12)} { − 5, 0, 5, 10, 15} How To Given a function written in equation form, find the domain Identify the input values Identify any restrictions on the input and exclude those values from the domain Write the domain in interval form, if possible Finding the Domain of a Function Find the domain of the function f(x) = x2 − The input value, shown by the variable x in the equation, is squared and then the result is lowered by one Any real number may be squared and then be lowered by one, so there are no restrictions on the domain of this function The domain is the set of real numbers In interval form, the domain of f is ( − ∞, ∞) Try It Find the domain of the function: f(x) = − x + x3 ( − ∞, ∞) How To 5/46 Domain and Range Given a function written in an equation form that includes a fraction, find the domain Identify the input values Identify any restrictions on the input If there is a denominator in the function’s formula, set the denominator equal to zero and solve for x If the ...Amgraf, Inc. PDF Conference 2005 Page 1 of 10 PDF Forms and Database Connectivity Solutions By Franklin J. Garner, III President and CEO Amgraf, Inc. September 26, 2005 Introduction Every company and organization uses business forms, and now most have PC’s with access to the Internet. With great software like Amgraf OneForm Designer Plus (OFDP) and Adobe Acrobat, paper forms can be converted to Internet forms (I-forms) thereby saving significant costs in printing and storage. With additional effort, I-forms can be extended into fillable, submittable containers for data capture, retrieval, presentation, and processing. The benefits of database-connected I-forms solutions include improvements in productivity, transaction accuracy, and user satisfaction. So where’s the problem? Forms layout and design, and even the steps to insert fill fields, are usually graphic designer tasks. A non-connected PDF form is a self-contained file with everything packaged within the visual image. To make an I-form submittable, the originator must go beyond the form image and interact with software for field data extraction, data communication with acknowledgement, and navigational methods to start and end the form filling session. These functions have traditionally been performed by computer programmers, and are worrisome tasks for graphic designers. Adding database connectivity also introduces another layer of complexity onto I-forms. This white paper is intended to clarify the technical issues involved in implementing an I-forms data collection and retrieval system. Basic Internet Forms Functionality Internet forms can be used for many online transaction functions. The starting point is where the image of a form is converted so that it can be displayed on a computer screen and output to a local printer. Most Acrobat Distiller users have mastered this conversion step, and many web sites now have links to PDF forms for user access. Upon clicking a link, the free Adobe Reader opens within the browser window and a PDF form is displayed. The form can then be locally saved and/or printed. Amgraf, Inc. PDF Conference 2005 Page 2 of 10 With the Amgraf OFDP and Adobe Acrobat software, the form owner or originator can add many other functions to make PDF forms: • fillable • pre-populated • submittable • dynamic database views • field flattened Fillable forms have fill-fields overlaid on the form background so that field information can be keyed. Fields can be coded so that input validation occurs immediately, helping to reduce errors. With a little extra effort, fields can be programmed so that standard answers are chosen from drop-down lists, numerical amounts are immediately calculated, and other input values are automatically tested for correctness. Pre-populated forms open at the client PC with many fields already filled in. Field data can be transmitted along with the PDF file as Forms Data Format (FDF) instructions, or merged with the PDF form before it is served to the client. By pre-populating fields, the client is relieved of the burden of re-keying information already on file, and assured that the central system knows who is on the other end of the transaction. Submittable forms move field data in the other direction, from the client to the server. When a form is filled out, the information can be transmitted to the server so that it can be saved and/or processed immediately, without the need to rekey or scan in keystrokes from a paper document image. The benefit is that the costs associated with handling forms can be greatly reduced. Dynamic Power and Authority Power and Authority Bởi: OpenStaxCollege The White House, one of the world’s most widely recognized state buildings, symbolizes the authority of the U.S presidency (Courtesy U.S National Archives/Wikimedia Commons) From the time of King Henry VIII to the time of Will and Kate, the role of the royal family in the British government has shifted dramatically Between those two eras—and across the Atlantic—former British subjects in what is now the United States fought for an alternative system of government one that left no room for royalty Despite these differences, governments play the same fundamental role: in some fashion, they exert control over the people they govern The nature of that control—what we will define as power and authority—is an important part of society Sociologists have a distinctive approach to studying governmental power and authority that differs from the perspective of political scientists For the most part, political scientists focus on studying how power is distributed in different types of political systems They would observe, for example, that the United States’ political system is divided into three distinct branches (legislative, executive, and judicial), and they would explore how public opinion affects political parties, elections, and the political process in general Sociologists, however, tend to be more interested in the influences of governmental power on society and in how social conflicts arise from the distribution of power Sociologists also examine how the use of power affects local, state, national, and global agendas, which in turn affect people differently based on status, class, and socioeconomic standing 1/9 Power and Authority What Is Power? Nazi leader Adolf Hitler was one of the most powerful and destructive dictators in modern history, pictured here with fascist Benito Mussolini of Italy (Photo courtesy of U.S National Archives and Records Administration) For centuries, philosophers, politicians, and social scientists have explored and commented on the nature of power Pittacus (c 640-568 B.C.E.) opined, “The measure of a man is what he does with power,” and Lord Acton perhaps more famously asserted, “Power tends to corrupt; absolute power corrupts absolutely” (1887) Indeed, the concept of power can have decidedly negative connotations, and the term itself is difficult to define Many scholars adopt the definition developed by German sociologist Max Weber, who said that power is the ability to exercise one’s will over others (Weber 1922) Power affects more than personal relationships; it shapes larger dynamics like social groups, professional organizations, and governments Similarly, a government’s power is not necessarily limited to control of its own citizens A dominant nation, for instance, will often use its clout to influence or support other governments or to seize control of other nation states Efforts by the U.S government to wield power in other countries have included joining with other nations to form the Allied forces during World War II, entering Iraq in 2002 to topple Saddam Hussein’s regime, and imposing sanctions on the government of North Korea in the hopes of constraining its development of nuclear weapons Endeavors to gain power and influence not necessarily lead to violence, exploitation, or abuse Leaders such as Martin Luther King Jr and Mohandas Gandhi, for example, commanded powerful movements that affected positive change without military force Both men organized nonviolent protests to combat corruption and injustice and succeeded in inspiring major reform They relied on a variety of nonviolent protest strategies such as rallies, sit-ins, marches, petitions, and boycotts Modern technology has made such forms of nonviolent reform easier to implement Today, protesters can use cell phones and the internet to disseminate information and 2/9 Power and Authority plans to masses of protesters in a rapid and efficient manner In Tunisia Fulbright Economics Teaching Program 2006-2007 Trade: Institutions and impact Ari Kokko 1 Lecture 1 Ari Kokko TRADE: INSTITUTIONS AND IMPACT Why and how do countries trade? Outline and schedule Ari Kokko Why do countries trade? • Get goods and services that cannot be produced at home • To accumulate gold • Get cheaper goods and services • Efficiency and growth • Different theories and policies for different motives Fulbright Economics Teaching Program 2006-2007 Trade: Institutions and impact Ari Kokko 2 Lecture 1 Ari Kokko Gains from trade: the simple view • Clear gains if countries are strong in different areas: absolute advantages • Less obvious - but undisputed - gains even if one country is “better” in all areas: comparative advantages Ari Kokko Absolute advantages Motorbikes Rice Vietnam 20 10 Laos 10 20 Labor requirements for one unit of output Fulbright Economics Teaching Program 2006-2007 Trade: Institutions and impact Ari Kokko 3 Lecture 1 Ari Kokko Comparative advantages Motorbikes Rice Vietnam 20 10 Laos 100 20 Labor requirements for one unit of output Ari Kokko Comparative advantages  Trade is profitable as soon as relative prices differ between countries  Why are there differences in relative prices?  Classical and neoclassical theory: – technology differences (Adam Smith 1776 / David Ricardo 1815) – differences in factor endowments (Heckscher- Ohlin 1930) Fulbright Economics Teaching Program 2006-2007 Trade: Institutions and impact Ari Kokko 4 Lecture 1 Ari Kokko Policy conclusions: neoclassical theory  Free trade and specialization is optimal  pattern of comparative advantages is given by nature  all industries are equally “desirable”  International framework should support development of free trade  unilateral liberalization more difficult because of protectionist interest groups and lack of coordination Ari Kokko Institutions: Bretton-Woods solutions  Four cornerstones of international economy after WWII to support growth of free trade – International Bank for Reconstruction and Development – International Monetary Fund – International Trade Organization – Price stabilization fund Fulbright Economics Teaching Program 2006-2007 Trade: Institutions and impact Ari Kokko 5 Lecture 1 Ari Kokko But why is world trade not free? • Protectionism leads to higher prices, lower consumption, and lower welfare both at home and abroad . • …so why is there still a lot of protectionism? Ari Kokko Unequal gains from trade at the micro level • Interest groups matter: trade benefits some groups but hurts others • trade raises the rewards of a country’s abundant factor of production and reduces the rewards of the scarce factor (Stolper-Samuelson theorem) • the groups that lose may oppose free trade • the transition to free trade may have troublesome social consequences Fulbright Economics Teaching Program 2006-2007 Trade: Institutions and impact Ari Kokko 6 Lecture 1 Ari Kokko Shortcomings in neoclassical trade theory  What if the assumptions of the neoclassical theory aren’t true? – all industries are not equally valuable: better to produce micro chips than potato chips – comparative advantages can be created: economies of scale and agglomeration effects Ari Kokko Modern trade theory  Economies of scale – Bigger is better – Hard to manage in free trade environment if American and Japanese companies will always be stronger  Need to manipulate comparative advantages – Strategic trade policy? Fulbright Economics Teaching Program 2006-2007 Trade: Institutions and impact Ari Kokko 7 Lecture 1 Ari Kokko Why strategic trade policy may be useful in theory • The location of industries with scale economies / agglomeration effects may be determined by history Taste and Smell Taste and Smell Bởi: OpenStaxCollege Taste, also Fulbright Economics Teaching Program 2006-2007 Trade: Institutions and impact Ari Kokko 1 Lecture 1 Ari Kokko TRADE: INSTITUTIONS AND IMPACT Why and how do countries trade? Outline and schedule Ari Kokko Why do countries trade? • Get goods and services that cannot be produced at home • To accumulate gold • Get cheaper goods and services • Efficiency and growth • Different theories and policies for different motives Fulbright Economics Teaching Program 2006-2007 Trade: Institutions and impact Ari Kokko 2 Lecture 1 Ari Kokko Gains from trade: the simple view • Clear gains if countries are strong in different areas: absolute advantages • Less obvious - but undisputed - gains even if one country is “better” in all areas: comparative advantages Ari Kokko Absolute advantages Motorbikes Rice Vietnam 20 10 Laos 10 20 Labor requirements for one unit of output Fulbright Economics Teaching Program 2006-2007 Trade: Institutions and impact Ari Kokko 3 Lecture 1 Ari Kokko Comparative advantages Motorbikes Rice Vietnam 20 10 Laos 100 20 Labor requirements for one unit of output Ari Kokko Comparative advantages  Trade is profitable as soon as relative prices differ between countries  Why are there differences in relative prices?  Classical and neoclassical theory: – technology differences (Adam Smith 1776 / David Ricardo 1815) – differences in factor endowments (Heckscher- Ohlin 1930) Fulbright Economics Teaching Program 2006-2007 Trade: Institutions and impact Ari Kokko 4 Lecture 1 Ari Kokko Policy conclusions: neoclassical theory  Free trade and specialization is optimal  pattern of comparative advantages is given by nature  all industries are equally “desirable”  International framework should support development of free trade  unilateral liberalization more difficult because of protectionist interest groups and lack of coordination Ari Kokko Institutions: Bretton-Woods solutions  Four cornerstones of international economy after WWII to support growth of free trade – International Bank for Reconstruction and Development – International Monetary Fund – International Trade Organization – Price stabilization fund Fulbright Economics Teaching Program 2006-2007 Trade: Institutions and impact Ari Kokko 5 Lecture 1 Ari Kokko But why is world trade not free? • Protectionism leads to higher prices, lower consumption, and lower welfare both at home and abroad . • …so why is there still a lot of protectionism? Ari Kokko Unequal gains from trade at the micro level • Interest groups matter: trade benefits some groups but hurts others • trade raises the rewards of a country’s abundant factor of production and reduces the rewards of the scarce factor (Stolper-Samuelson theorem) • the groups that lose may oppose free trade • the transition to free trade may have troublesome social consequences Fulbright Economics Teaching Program 2006-2007 Trade: Institutions and impact Ari Kokko 6 Lecture 1 Ari Kokko Shortcomings in neoclassical trade theory  What if the assumptions of the neoclassical theory aren’t true? – all industries are not equally valuable: better to produce micro chips than potato chips – comparative advantages can be created: economies of scale and agglomeration effects Ari Kokko Modern trade theory  Economies of scale – Bigger is better – Hard to manage in free trade environment if American and Japanese companies will always be stronger  Need to manipulate comparative advantages – Strategic trade policy? Fulbright Economics Teaching Program 2006-2007 Trade: Institutions and impact Ari Kokko 7 Lecture 1 Ari Kokko Why strategic trade policy may be useful in theory • The location of industries with scale economies / agglomeration effects may be determined by history Sex and Sexuality Sex and Sexuality Bởi: OpenStaxCollege Sexual ... then subtracted from the result The domain is ( − ∞, ∞) and the range is also ( − ∞, ∞) 24/46 Domain and Range Finding the Domain and Range Find the domain and range of f(x) = x + We cannot evaluate... to the top of the graph for range Finding Domain and Range from a Graph Find the domain and range of the function f whose graph is shown in [link] 12/46 Domain and Range We can observe that the... smallest and largest values since they not fall exactly on the grid lines Try It Given [link], identify the domain and range using interval notation 14/46 Domain and Range domain =[1950,2002] range

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