...Name of function: CONSTANT Symmetry: y-axis Equation: Max: none Calculator Notation: y=2 Min: none Domain: all real #’s Increasing: none Range: y=2 Decreasing: none X – Intercept: none Vertical Asymptotes: none Y – Intercept: (0, 2) Horizontal Asymptotes: none Table: x y -1 2 0 2 1 2 Name of function: LINEAR Symmetry: origin Equation: Max: none Calculator Notation: y=x Min: none Domain: all real #’s Increasing: (-,) Range: all real #’s Decreasing: none X – Intercept: (0, 0) Vertical Asymptotes: none Y – Intercept: (0, 0) Horizontal Asymptotes: none Table: x y -2 -2 -1 -1 0 0 1 1 2 2 Name of function: QUADRATIC Symmetry: y-axis Equation: Max: none Calculator Notation: y=x^2 Min: (0, 0) Domain: all real #’s Increasing: (0,) Range: y ≥ 0 Decreasing: (-, 0) X – Intercept: (0, 0) Vertical Asymptotes: none Y – Intercept: (0, 0) Horizontal Asymptotes: none Table: x y -2 4 -1 1 0 0 1 1 2 4 Name of function: CUBIC Symmetry: origin Equation: Max: none Calculator Notation: y=x^3 Min: none Domain: all real #’s Increasing: (-,) Range: all real #’s Decreasing: none X – Intercept: (0, 0) Vertical Asymptotes: none Y – Intercept: (0, 0) Horizontal Asymptotes: none Table: x y -2 -8 -1 -1 0 0 1 1 2 8 Name of function: ABSOLUTE VALUE Symmetry: y-axis Equation: Max: none Calculator Notation: y=abs(x) Min: (0, 0) Domain: all real #’s...
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...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 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. An equation whose graph is a straight line is called a linear function (y = mx + c). * Consider this Example 1: * Using descriptive variables, we choose k for kilometers and R for Cost in Ringgit Malaysia as a function of miles: R(k). * We know for certain that R(0) = 3.30, since the RM3.30 drop charge is assessed regardless of how many kilometers are driven. * Since RM2.40 is added for each kilometer driven, then: R(1) = 3.30 + 2.40 = 5.70. * If we then drove a second kilometer, another RM2.40 would be added to the cost: R(2) = 3.30 + 2.40 +2.40 = 8.10. * If we drove...
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...4-1 Exponential Functions 1. What is the definition of an exponential function? Page 412 An exponential function f with base b is defined by f(x) = bx or y = bx, where b is a positive constant other than 1 (b > 0 and b is not equal to 1) and x is any real number. Example: g(x) = 10^x 2. What is the inverse of an exponential function? Page No horizontal line can be drawn that intersects the graph of an exponential function at more than one point. This means that the exponential function is one-to-one and has an inverse. Example: fx = b(x) Steps for solving problem: Replace: fx with y: y = b(x) Interchange x and y: x=b(y) Solve for y 3. What are the characteristics of an exponential function? Page 415 * The domain of f(x) = b^x consists of all real numbers. The range of F(x) = b^x consists of all positive real numbers (0, to infinity). * The graphs of all exponential functions of the form f(x) = b^x pass Through the point (0, 1) because f(0) = b^0 =1 (b not equal to 0) the y intercept is 1. There is no x intercept. * If b > 1, f(x) – b^x has a graph that goes up to the right and is an increasing function. The greater the value of b, the steeper the increase. * If 0 < b < 1, f (x) = b^x has a graph that goes down to the right and is a decreasing function. The smaller the value of b, the steeper the decrease. * F(x) = b^x is one-to-one...
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... * Patriots – Tom Brady * Rams – Joe Namath * Chiefs – Joe Montana 1. Using D as the domain and Q as the range, show the relation between the 2 sets, with the correspondences based on which players are on which team. Show the relation in the following forms: Set of ordered pairs (20 points) Directional graph (like the pictures draw in class in our live chats – see HINT below). (20 points) The ordered pairs when D is the domain are: {(Jets,Joe Namath),(Giants,Eli Manning),(Cowboys, Troy Aikman),(49ers,Joe Montana),(Patriots,Tom Brady),(Rams,Joe Namath),(Chiefs, Joe Montana)} 2. Is the relation a function? Explain. (10 points) This is a function, because every element (Quarterback) of the domain is mapped to exactly one unique element (Team) of the range. So with the one to one relation of player to team, that makes this a function. 3. Now, use set Q as the domain, and set D as the range (reverse). Show the relation in the following forms: Set of ordered pairs (20 points) Directional graph (20 points) The ordered pairs when Q is the domain are: {(Joe Namath, Jets),(Eli Manning, Giants),( Troy Aikman, Cowboys),( Joe Montana,49ers,),(Tom Brady, Patriots),(Joe Namath, Rams),(Joe...
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...The Application of the Profit Function in a Business’s Growth Differential Calculus May 24, 2014 The application of calculus in a business is extremely important since calculus is considered as the study of changes. Its complexity in the study of changes has become one of the humankind’s greatest tool for analyzing changes in the marketplace. The profit function was created with the main purpose for businesses to understand how the changes in revenues and in costs would generate a profit or not profit at all. A profit can be generated when the amount of revenues is higher than the amount of costs. When a business starts, is normal to not gain any profit at all, in fact, most of the time, a business tends to lose money in its first year. However with that information, a business can analyze the money loss of that year and determine any gaps or holes that prevents the maximization of the profit and have a more prosperous result for the following year. For instance, if a company suffer a loss in profit, they can analyze the profit function to determine the main reason of why there was not a positive profit. If they see that the problem of the profit function was a low revenue then they can regulate the sale of products or services and price control, or if the problem lies in the cost function, they can adjust or lower the costs and expenses made by the business. The graph of a profit function can show at what time of the year the company tends to...
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...The Production Function for Wilson Company By using the EViews software, we get the result below by using Least Square method: Dependent Variable: Y | | | Method: Least Squares | | | Date: 06/18/12 Time: 03:24 | | Sample: 1 15 | | | Included observations: 15 | | | | | | | | | | | | Variable | Coefficient | Std. Error | t-Statistic | Prob. | | | | | | | | | | | C | -130.0086 | 129.8538 | -1.001192 | 0.3365 | L | 0.359450 | 0.245593 | 1.463601 | 0.1690 | K | 0.027607 | 0.006051 | 4.562114 | 0.0007 | | | | | | | | | | | R-squared | 0.838938 | Mean dependent var | 640.3800 | Adjusted R-squared | 0.812094 | S.D. dependent var | 227.9139 | S.E. of regression | 98.79645 | Akaike info criterion | 12.20086 | Sum squared resid | 117128.9 | Schwarz criterion | 12.34247 | Log likelihood | -88.50643 | F-statistic | 31.25263 | Durbin-Watson stat | 1.458880 | Prob(F-statistic) | 0.000017 | | | | | | | | | | | 1. In standard form the estimated Cobb-Douglas equation is written as: Q= α Lβ1 Kβ2 The multiplicative exponential Cobb-Douglass Function can be estimated as a linear regression relation by taking logarithm: Log Q = log α + β1 log L + β2 log K Therefore: log(y) = -130.0086 + 0.359450*log(L) + 0.027607*log(K) The output elasticity of capital is 0.027607 and the output elasticity of labor is 0.359450. 2...
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...Exercise 1 Worksheet: Features and Functions Table Save this worksheet to your computer with the filename "Your_Name_Exercise_1." Complete the table below comparing the Online Learning System (OLS) classroom with the New Classroom by doing the following: Find the corresponding feature or function in New Classroom that most closely matches the one listed for OLS. Explain how each feature or function influences your learning experience. Submit the completed worksheet as an attachment via the Assignment tab. |OLS Feature or Function |Which New Classroom feature or function most |How does this feature or function support your | | |closely matches the OLS feature or function? |learning experience? | |Main forum |The main forums are no longer necessary in new |It support my learning experience by display | | |classroom, because there are no main, private,or|the full calendar week of assignments, messages | | |learning team forums in the new classroom. |and learning activities. | |Individual forum |The Individual forum are know situated below the|This allows the students to communicate in | | |discussion box. |private with your instructor. | |Syllabus |The...
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...SPECIAL POINTS OF INTEREST: Study Habits Test Taking B Y : J A S P A R T A P B A L J A N U A R Y 2 6 , 2 0 1 6 Big Ideas The Tribune Skills Leverage Learning Welcome To Advance Functions This article will discuss several aspects that will allow you to be successful in the course. from the previous semester to get the previous year’s tests. After finishing the test review, try the test questions; if you are able to solve the test questions then you have successfully prepared for the test. Big Ideas of the Course There is a ton of content that will be taught in this course. Be sure to take notes regularly and copy all examples that are explained in the classroom. In this course you will learn things such as graphing reciprocal as well as rational functions; graphing sine, cosine, and tangent functions; proving trigonometric identities; graphing exponential growth and logarithmic functions. These ideas are barely touched in grade 11 functions but taught with detail in grade 12. Be sure to brush up on graphing before the beginning of the course because it will help you throughout the course. Study Habits Be sure to come to class everyday and on time. It can’t be stressed enough that missing class will result in failure. Get connected. If you happen to miss a class talk to your peers and keep up with homework. Make sure that you do your homework and clarify any questions with the teacher...
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...Most of the functions we have studied have been polynomial or rational functions, with a few others involving roots of polynomial or rational functions. Functions that can be expressed in terms of addition, subtraction, multiplication, division, and the taking of roots of variables and constants are called algebraic functions. In exponential & logarithmic functions we introduce and investigate the properties of exponential functions and Logarithmic functions. These functions are not algebraic; they belong to the class of transcendental functions. Exponential and logarithmic functions are used to model a variety of realworld phenomena: growth of populations of people, animals, and bacteria; radioactive decay; epidemics; absorption of light as it passes through air, water, or glass; magnitudes of sounds and earthquakes. We consider applications in these areas plus many more in the sections very important. As a part of our BBA course, we are required to submit a term paper for every subject each semester. As our Advance Business Mathematics faculty Associate Professor Lt. Col. Md. Showkat Ali has asked us to submit a term paper on a topic upon our will. So, we have decided to choose “Exponential & Logarithmic Functions”. to graph exponential functions to evaluate functions with base e to learn the use of compound interest formulas to learn the changing from logarithmic to exponential form to learn the changing from exponential...
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...Function Point Analysis How to use this document...................................................................................... 1 1 Introduction ......................................................................................................... 2 2 Measures Derived from FPA ............................................................................... 2 3 Different FPA Methods ....................................................................................... 2 4 The advantages of using FPA............................................................................. 3 5 The disadvantages of, or problems using, FPA .................................................. 3 6 Developed v Delivered FPs................................................................................. 4 7 The use of FPs in estimating effort and cost ...................................................... 5 8 Function Point counting procedure ..................................................................... 6 8.1 IFPUG Method ............................................................................................. 6 8.1.1 Complexity Matrices............................................................................... 7 8.1.2 Complexity/UFP Contribution................................................................. 7 8.1.3 Overall FP Count ................................................................................... 8 8.1.4 IFPUG FPA Process Summary..........................
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...Real World Quadratic Functions Christine Sandoval MAT222: Intermediate Algebra (ACR1438C) Instructor: Yvette Gonzalez-Smith October 10, 2014 Real World Quadratic Functions In some types of business being able to solve real world quadratic functions are very important. When we think about the quadratic curves I would point to curves known as the circle, ellipse, hyperbola and parabola (Dugopolski, 2012). I at first thought this was something that came about during my time but these actual quadratic curves came about during the ancient Greek times but they now have more real world applicability than one would think. Quadratic equations described the orbits where the planets moved round the Sun but also furthered advances in astronomy (Budd & Sangwin, 2004). A long time ago Galileo found some type of link between quadratic equations and acceleration (2004). I would believe that being able to solve real world quadratic problems are important in business because we should be able to show a return on investment or profit. We need to be able to analyze the accounts payable and receivable to determine how the business looks. Quadratic functions are not only used in business they are used in science and engineering just to name a couple of areas. Our task today is not only to show how important it is to understand quadratic functions but also to explain how important they are in business. When we think about quadratic functions we may think about the u-shape of the parabola...
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...Linear Functions Unit Plan Part 2 – EDCI 556 – Week 2 Darrell Dunnas Concordia University, Portland Linear Functions Unit Plan Part 2 Mr. Dunnas decides to change the graphing linear equations lesson into a problem-based lesson. This lesson is comprised of three components. Component number one is to write the equation in slope-intercept form (solve for y). Component number two is to find solutions (points) to graph via t-tables and slope-intercept form. Component number three is to graph the equation (connect the points that form a straight line). In mastering this lesson, all components must be addressed. In teaching, all learners how to graph linear equations, one must create a meaningful context for learning. First, the lesson must be aligned to the curriculum framework (Van de Walle, Karp, & Bay-Williams, 2013). Graphing linear equations is a concept found in the curriculum framework. Second, the lesson must address the needs of all students (Van de Walle, Karp, & Bay-Williams, 2013). The think-aloud strategy and graphing calculators will be used to graph linear equations and address the learning styles of all learners. Third, activities or tasks must be designed, selected, or adapted for instructional purposes (Van de Walle, Karp, & Bay-Williams, 2013). Lectures, handouts, videos, and cooperative learning activities will be used in teaching the lesson. Fourth, assessments must be designed to evaluate the lesson...
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...Quality Function Deployment of Custom Orientation Stabilization Integrated Systems September 23, 2012 Scott Jaster ENM5100 Quality Engineering Florida Institute of Technology ABSTRACT The purpose of this paper is to present a description of the Quality Function Deployment (QFD) process with respect to the development of an alternative means of multi-axis orientation stabilization. The intention is to discuss the quality control process of choosing the "best" components for the system, and meeting customer requirements before, during, and after product delivery. There will be an exploration of the Quality Function Deployment (QFD) process that pertains to the systems integration design, manufacture, and delivery process, from the user’s ultimate perspective. The interactions of the various components must be defined by the desired specifications, modeled, and analyzed to produce the optimal setup that meets the respective performance requirements of the user, while following along with the QFD process strategy. The focus will be on the House Of Quality (HOQ), described within. A related discussion will be the determination of the viability and functionality of designing a system capable of efficiently counteracting axial orientation wobbling; but this is the byproduct of the properly employed functional Quality process. Ultimately, the discussed Quality process allows the user to efficiently and subjectively determine the best engineering trade-offs related...
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...operations on real numbers and polynomials and simplify algebraic, rational, and radical expressions. Arithmetic and geometric sequences are examined, and linear equations and inequalities are discussed. Students learn to graph linear, quadratic, absolute value, and piecewise-defined functions and solve and graph exponential and logarithmic equations. Other topics include solving applications using linear systems as well as evaluating and finding partial sums of a series. Course Objectives After completing this course, students will be able to: ● Identify and then calculate perimeter, area, surface area, and volume for standard geometric figures ● Perform operations on real numbers and polynomials. ● Simplify algebraic, rational, and radical expressions. ● Solve both linear and quadratic equations and inequalities. ● Solve word problems involving linear and quadratic equations and inequalities. ● Solve polynomial, rational, and radical equations and applications. ● Solve and graph linear, quadratic, absolute value, and piecewise-defined functions. ● Perform operations with functions as well as find composition and inverse functions. ● Graph quadratic, square root, cubic, and cube root functions. ● Graph and find zeroes of polynomial...
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...product of the set of real numbers and itself? Ans : The Cartesian product is every ordered pair in all of the quadrants of the coordinate plane. 2. What is the domain and range of the relation {(2, 4),(4, 8),(8, 16)} ? Ans: domain {2,4,8} and range {4,8,16} and the function can be given as f(x)=2x. 3. Decide whether the graph below is a function. Ans: The above shown graph is not a function since for a given x value it has multiple y values at certain points and hence cannot be a function. 4. What is the domain and range of the function f (x) = ? Ans: domain 0 ≤ x and range 0 ≤ f(x) 5. Is the following a function: y = ± x ? Ans : No it is not a function for a given x value it has two Y values . 6. Is the function f (x) = 4x even, odd, or neither? Ans : function f (x) = 4x is an odd function since f (x) = - f (- x) 7. Is the function f (x) = x - 5 even, odd, or neither? Ans : function f (x) = x - 5 is neither neither even nor odd. 8. What is the inverse of the function y = , and is it a function? Ans : The inverse is y = x2 +1 and It is a function. 9. A piecewise function is defined this way: f (x) = - x for x < 0 , f (x) = x2 for 0 ≤ x ≤ 3 , f (x) = 3x for x > 3 . What is f (- 4) + f (3) + f (7) ? Ans : -4 + 9...
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