CHAPTER 4 : FUNCTIONS AND THEIR GRAPHS 4.1 Definition of Function A function from one set X to another set Y is a rule that assigns each element in X to one element in Y. 4.1.1 Notation If f denotes a function from X to Y‚ we write 4.1.2 Domain and range X is known as the domain of f and Y the range of f. (Note that domain and range are sets.) 4.1.3 Object and image If and ‚ then x and y are known respectively as the objects and images of f. We can write ‚ ‚ . We can represent
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Graphs 1‚ 2‚ 3‚ and 4 show the waveforms for the flute‚ violin‚ piano‚ and oboe. The Fourier Series can be used to explain why each of the instruments have their own unique sound. The flute‚ violin‚ piano and oboe have different combinations of frequencies as each waveform is made of an unique combination of sine and cosine waves‚ and this creates distinct waveforms and allows each instrument to have a unique sound. Recall that the formula of the Fourier Series is f(x)=a_0+∑_(k=1)^∞▒(a_k cos〖πkx/T〗+b_k
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line on a Cartesian graph is approximately the distance y in feet a person walks in x hours. What does the slope of this line represent? How is this graph useful? Provide another example for your colleagues to explain. The slope of the line represents the speed of the person in feet per hour. This graph is useful because it provides a visual representation of the continuous motion of the person walking‚ something that could not provided by something like a bar graph. In a bar graph‚ the sheer number
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Misleading Graphs Team C Introduction to Statistics—QNT/273 February 7‚ 2011 Jeffrey McDonough Misleading Graphs “Graphs give a visual representation that enables readers to analyze and interpret data more easily than they could simply by looking at numbers. However‚ inappropriately drawn graphs can misrepresent the data and lead the reader to false conclusions” (Bluman‚ 2009‚ p.76). Some methods used by graph makers to mislead consumers are truncated axis starting points and using two
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NAME_________________________________ STAMP________________ PERIOD____ PICTURES & GRAPHS A. The Atom 1. Calculate the average atomic mass using the spectrum below. 2. Answer the questions regarding the energy level diagram shown. a) The emission lines for the series above are in the IR‚ Vis and UV regions. Match the series with the region and justify your choice (FYI – AP you do not need to memorize the names of the series. IB will need to know then for next year). b) Would the wavelength
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Essay and report writing This table has been constructed to illustrate the main differences between the sections to be contained within reports compared to the format of essays. Report Title page: Name‚ tutor’s name‚ course title‚ date List of contents: Titles of main sections of report with page numbers Introduction: (approx. 10% of word count) Purpose and content of the report An outline of what the piece of research is about and its importance or significance Definitions of terms Essay Title
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Graph theory - the study of graphs and networks‚ is often considered part of combinatorics‚ but has grown large enough and distinct enough‚ with its own kind of problems‚ to be regarded as a subject in its own right.[12] Graphs are one of the prime objects of study in discrete mathematics. They are among the most ubiquitous models of both natural and human-made structures. They can model many types of relations and process dynamics in physical‚ biological and social systems. In computer science‚
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There are some basic differences between a report and an essay in an academic setting. The format of a report and essay differ as well as the main purpose of each. While there are similarities and differences between an essay and report‚ it’s essential to know which format you’re being asked to write. First‚ we’ll discuss what a report is‚ and then continue on to see what makes an essay. Keep in mind that a report can be much longer than an essay‚ and report readers generally only quickly scan it to
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totally free essay resources online that are designed to provide professionally written papers for those who are in need of essay-writing help or inspiration. These sites provide papers that are written in any style‚ with proper word usage‚ grammar and sentence structure. The essays are written to the style of the desired topic and also provide a list of citations‚ an annotated bibliography‚ or a complete literature review depending on the subject material of the essay. Some of the free essays available
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