Week 1 Linear Functions * As you hop into a taxicab in Kuala Lumpur, the meter will immediately read RM3.30; this is the “drop” charge made when the taximeter is activated. After that initial fee, the taximeter will add RM2.40 for each kilometer the taxi drives. In this scenario, the total taxi fare depends upon the number of kilometer ridden in the taxi, and we can ask whether it is possible to model this type of scenario with a function. As you hop into a taxicab in Kuala Lumpur, the meter
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Managerial Mathematics(QQM 1023) Tutorial 2 – Introduction to Function 1. Which of the following equations define y as a function of x? a) y = 3x + 1 b) y = 2x2 c) y = 5 d) y = 2x e) x = 3 f) y2 = x g) y = x3 h) y = [pic] i) y = x j) y = [pic] 2. Determine types of function for the following equations: a) f(x) = 2 b) g(x) = [pic] c) f(x) = 4 – x d) f(x) = 2x e) g(x) = x2 + 3x f) h(x) = 2x
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Contents 0. Preface 1. Functions and Models 1.1. Basic concepts of functions 1.2. Classification of functions 1.3. New functions from old functions 1 2 2 5 8 0. Preface Instructor: Jonathan WYLIE, mawylie@cityu.edu.hk Tutors: Radu Gogu, rgogu2@student.cityu.edu.hk. Texts: Single Variable Calculus, by James Stewart, 6E. In this semester, we will cover the majority of Chap 1-4, 7, 12. Upon completion of this course, you should be able to understand limit, derivatives, and its applications in mathematical
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Honors Algebra II Supplemental Notes Oblique Asymptotes Key Concepts: An oblique asymptote is an oblique, or slanted, line that the graph of a function approaches, but never touches, as x → ∞ ( x approaches infinity). To find the oblique asymptote of a rational function: 1. Reduce the rational function P( x) to lowest terms. An oblique asymptote can be found Q( x) when the degree of P ( x) is one greater than the degree of Q ( x ) . c 2. Divide P ( x) by Q ( x ) using long division to get
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the set of integers and[pic]. F(x) is a one-to-one function if we can show that: For [pic] and[pic], [pic]=[pic]===> [pic]=[pic] Let’s find out: [pic]==> [pic]=[pic], and [pic]=[pic] So, [pic]=[pic]==> [pic]=[pic]. Subtracting 101 on both sides gives [pic]==> [pic]=[pic]. Since we’re able to show that [pic]=[pic] ==> [pic]=[pic], we then conclude that [pic] is a one-to-one function. 2. Let’s prove that [pic] is a one-to-one function. To prove that, we have to show that For [pic] and[pic]
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small and simple circuits • Express a switching function of n variables as a composition of switching functions of less than n variables Motivation: • Reduce the complexity of simplification • Reduce the size of a circuit by finding common circuit elements Theoretical background: • Shannon’s Expansion Theorem (SET): – Simple type of decomposition – f(x1, x 2, ..., xn) = x 1f(1, x 2, ..., xn) + x’1 f(0, x 2, ..., xn) 1 Residues • The function that is obtained from setting one of the variables
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some Maple work. 1. Solve the following inequalities: a) b) c) 2. Appendix D #72 3. Consider the functions and . a) Use a Maple graph to estimate the largest value of at which the graphs intersect. Hand in a graph that clearly shows this intersection. b) Use Maple to help you find all solutions of the equation. 4. Consider the function. a) Find the domain of. b) Find and its domain. What is the range of? c) To check your result in b), plot and
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Exam Name___________________________________ Practice Math 55 Final I will drop 45 problems before the final draft MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Solve. 1) - 1 1 < x-5 3 9 1 3 A) (-48, -42] 1) B) (42, 48] C) [2, -2) D) (2, 8] 2) A plane traveling 410 mph in still air encounters a 65-mph headwind. How long will it take the plane to travel 675 mi into the wind? Round your answer to the nearest
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x 2 D. [0, ] 2. Describe how the graph of y = f(x-2)+1 is obtained from graph of y = f(x). A. 2 left, then 1 up. Bộ môn Toán, ĐH FPT Hà Nội B. 2 right, then 1up. A. x = -1 C. y = -3 D. y = 3 10. Find c so that the function is continuous on R x 2 cx c 1 if g ( x) x 1 2 if x 1 C. 2 right, then 1 down. D. 2 left, then 1 down. 3. Let B. x = 2 f ( g ( x)) 2x 3. Then: A. f ( x) x , g ( x) 2x 3. A. 0 B. f ( x)
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Student Solutions Manual for SINGLE VARIABLE CALCULUS rS al e SEVENTH EDITION DANIEL ANDERSON University of Iowa Fo JEFFERY A. COLE Anoka-Ramsey Community College N ot DANIEL DRUCKER Wayne State University Australia . Brazil . Japan . Korea . Mexico . Singapore . Spain . United Kingdom . United States ALL RIGHTS RESERVED. No part of this work covered by the copyright herein may be reproduced, transmitted, stored, or used in any form or by any means graphic
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