The document provides instructions for a case study analysis assignment on ethics and social responsibility. Students are asked to analyze issues of integrity, ethics, and social responsibility in a provided case study about a woman who was sexually harassed and sued her company. They must discuss the ethical theories and options available to the woman, support their arguments with additional research, and discuss any ethical justifications the company could use. The assignment must be 1000-1500 words and follow Harvard referencing style. It will be worth 30% of the student's grade.
This document introduces the concept of functions and relations. It defines a relation as a set of ordered pairs where the domain is the set of first elements and the range is the set of second elements. Relations can be defined by tables, graphs, equations or correspondences. The document provides examples of finding the domain and range of relations defined in various ways. It also gives an example of using a linear relation between femur length and height to estimate a person's height from skeletal remains.
This document provides an overview of functions and continuity. It begins with essential questions about determining if functions are one-to-one and/or onto, and determining if functions are discrete or continuous. The document then defines key vocabulary terms related to functions, including one-to-one functions, onto functions, discrete relations, continuous relations, and more. It provides examples to demonstrate these concepts, such as evaluating functions, graphing equations, and determining if a relation represents a function.
This document provides an overview of constraint satisfaction problems (CSPs). It defines a CSP as a problem where variables must be assigned values from their domains to satisfy constraints. Examples of CSPs include the n-queens puzzle, map coloring, Boolean satisfiability, and cryptarithmetic problems. A CSP is represented as a constraint graph with nodes as variables and edges as binary constraints. The goal is to assign values to each variable to satisfy all constraints.
The document discusses propositional logic as a knowledge representation language. It defines key concepts in propositional logic including: syntax, semantics, validity, satisfiability, interpretation, models, and entailment. It explains that propositional logic uses symbols to represent facts about the world and connectives to combine symbols into sentences. Sentences can then be evaluated based on the truth values assigned to symbols to determine if the overall sentence is true or false. Propositional logic allows new sentences to be deduced from existing sentences through inference rules while maintaining logical validity.
A function is a rule that assigns each input exactly one output, so that each x-value relates to a single y-value. Functions can be represented numerically with ordered pairs, graphically with a set of points where no x-value appears twice, verbally through a word problem, and algebraically with an equation relating x and y. Checking for a single output for each input is important to determine if a relation represents a function.
This document provides an introduction to first-order logic (FOL) including motivation, syntax, semantics, and examples. It discusses how FOL allows statements about relationships between objects using predicates, constants, variables, and quantifiers. Interpretations assign meanings to symbols and determine whether formulas are true or false. Validity and entailment are defined in terms of interpretations satisfying formulas.
This document discusses propositional logic inference rules and their properties. It introduces several common rules of inference like modus ponens, and introduction, and elimination. It also discusses the relationship between inference and entailment, and defines important properties of soundness, completeness, and decidability for logical systems. Examples are provided to demonstrate proving goals using rules of inference and a truth table is used to check entailment.
Fuzzy logic allows for intermediate values between absolute true and false. It calculates degrees of membership and handles imprecise conditions like natural language. Areas that use fuzzy logic include appliances, expert systems, and automotive systems like antilock brakes. Fuzzy logic systems involve fuzzifying inputs, applying operators, implicating outputs, aggregating results, and defuzzifying outputs.
This document introduces the concept of functions and relations. It defines a relation as a set of ordered pairs where the domain is the set of first elements and the range is the set of second elements. Relations can be defined by tables, graphs, equations or correspondences. The document provides examples of finding the domain and range of relations defined in various ways. It also gives an example of using a linear relation between femur length and height to estimate a person's height from skeletal remains.
This document provides an overview of functions and continuity. It begins with essential questions about determining if functions are one-to-one and/or onto, and determining if functions are discrete or continuous. The document then defines key vocabulary terms related to functions, including one-to-one functions, onto functions, discrete relations, continuous relations, and more. It provides examples to demonstrate these concepts, such as evaluating functions, graphing equations, and determining if a relation represents a function.
This document provides an overview of constraint satisfaction problems (CSPs). It defines a CSP as a problem where variables must be assigned values from their domains to satisfy constraints. Examples of CSPs include the n-queens puzzle, map coloring, Boolean satisfiability, and cryptarithmetic problems. A CSP is represented as a constraint graph with nodes as variables and edges as binary constraints. The goal is to assign values to each variable to satisfy all constraints.
The document discusses propositional logic as a knowledge representation language. It defines key concepts in propositional logic including: syntax, semantics, validity, satisfiability, interpretation, models, and entailment. It explains that propositional logic uses symbols to represent facts about the world and connectives to combine symbols into sentences. Sentences can then be evaluated based on the truth values assigned to symbols to determine if the overall sentence is true or false. Propositional logic allows new sentences to be deduced from existing sentences through inference rules while maintaining logical validity.
A function is a rule that assigns each input exactly one output, so that each x-value relates to a single y-value. Functions can be represented numerically with ordered pairs, graphically with a set of points where no x-value appears twice, verbally through a word problem, and algebraically with an equation relating x and y. Checking for a single output for each input is important to determine if a relation represents a function.
This document provides an introduction to first-order logic (FOL) including motivation, syntax, semantics, and examples. It discusses how FOL allows statements about relationships between objects using predicates, constants, variables, and quantifiers. Interpretations assign meanings to symbols and determine whether formulas are true or false. Validity and entailment are defined in terms of interpretations satisfying formulas.
This document discusses propositional logic inference rules and their properties. It introduces several common rules of inference like modus ponens, and introduction, and elimination. It also discusses the relationship between inference and entailment, and defines important properties of soundness, completeness, and decidability for logical systems. Examples are provided to demonstrate proving goals using rules of inference and a truth table is used to check entailment.
Fuzzy logic allows for intermediate values between absolute true and false. It calculates degrees of membership and handles imprecise conditions like natural language. Areas that use fuzzy logic include appliances, expert systems, and automotive systems like antilock brakes. Fuzzy logic systems involve fuzzifying inputs, applying operators, implicating outputs, aggregating results, and defuzzifying outputs.
The objective of this paper is to introduce a fuzzy linear programming problem with hexagonal fuzzy
numbers. Here the parameters are hexagonal fuzzy numbers and Simplex method is used to arrive an
optimal solution by a new method compared to the earlier existing method. This procedure is illustrated
with numerical example. This will further help the decision makers to come out with a feasible alternatives
with better economical viability.
Here are examples of the Associative Property and Commutative Property:
Associative Property:
Addition: (2 + 3) + 5 = 2 + (3 + 5)
Multiplication: 3 × (4 × 2) = (3 × 4) × 2
Commutative Property:
Addition: 2 + 5 = 5 + 2
Multiplication: 3 × 4 = 4 × 3
The Associative Property shows that changing the grouping of numbers or variables does not change the sum or product. The Commutative Property shows that changing the order of numbers or variables does not change the sum or product.
Fuzzy logic provides a means of calculating intermediate values between absolute true and absolute false. It allows partial set membership and handles imprecise data. Fuzzy logic systems use membership functions to determine the degree to which inputs belong to sets and fuzzy inference systems to map inputs to outputs. Fuzzy logic has applications in devices like washing machines and cameras that require handling imprecise variables.
This document provides an introduction to fuzzy logic and fuzzy sets. It discusses key concepts such as fuzzy sets having degrees of membership between 0 and 1 rather than binary membership, and fuzzy logic allowing for varying degrees of truth. Examples are given of fuzzy sets representing partially full tumblers and desirable cities to live in. Characteristics of fuzzy sets such as support, crossover points, and logical operations like union and intersection are defined. Applications mentioned include vehicle control systems and appliance control using fuzzy logic to handle imprecise and ambiguous inputs.
The document discusses identifying the domain and range of functions. The domain is the set of all x-coordinates in a relation, while the range is the set of all y-coordinates. A relation is a function if each element in the domain is mapped to only one element in the range - in other words, if each x-value has a single, unique y-value. The document provides examples of stating the domain and range of relations and determining whether they represent functions.
This document defines relations and functions in mathematics. A relation is a set of ordered pairs where the domain is the set of all x values and the range is the set of all y values. A function assigns each element in the domain (set of x values) to exactly one element in the range (set of y values). Functions are commonly represented by letters like f(x), where f denotes the name of the function and x is the variable. The left side of a function equation tells us the name and variable of the function, not that the function is being multiplied.
11.a new computational methodology to find appropriateAlexander Decker
This document proposes a new computational methodology for finding appropriate solutions to fuzzy equations of the form A=B, where A and B are known continuous triangular fuzzy numbers and X is an unknown fuzzy number. It introduces definitions of "positive fuzzy number," "negative fuzzy number," and "half-positive and half-negative fuzzy number." Several propositions and theorems are presented along with proofs to show that the solution to such a fuzzy equation can be a positive, negative, or half-positive/half-negative fuzzy number, depending on the values of A and B. Examples are provided to illustrate solving equations where A and B are positive, negative, or half-positive/half-negative fuzzy numbers. The methodology aims to overcome limitations
A new computational methodology to find appropriateAlexander Decker
This document proposes a new computational methodology for finding appropriate solutions to fuzzy equations of the form A=B, where A and B are known fuzzy numbers and X is an unknown fuzzy number. It introduces definitions of positive, negative, and half-positive/half-negative fuzzy numbers. Propositions and theorems are presented to show that the solution to such an equation can be a positive, negative, or half-positive/half-negative fuzzy number depending on the properties of A and B. Examples are provided to illustrate solving equations where A and B are positive, negative, or half-positive/half-negative fuzzy numbers. The methodology aims to overcome limitations in solving equations where X is an unknown fuzzy number.
The document discusses relations and functions. It provides examples of relations that are and are not functions using ordered pairs. A relation is a function if each element in the domain is mapped to exactly one element in the range. This is determined using a mapping diagram or by applying the vertical line test to a graphical representation of the relation.
The document defines functions and discusses:
- Functions are sets of ordered pairs with each first element paired to a unique second element.
- Functions can be one-to-one or many-to-one.
- Functions are represented in set notation, tabular form, as equations, and as graphs.
- The domain of a function is the set of first elements and the range is the set of second elements.
This document provides an overview of key concepts in algebra including:
- Evaluating algebraic expressions and using variables, formulas, and mathematical models.
- Foundational concepts of sets such as intersections, unions, and subsets of real numbers.
- Properties and applications of real numbers including the number line, inequalities, absolute value, and distance.
- Simplifying algebraic expressions by combining like terms.
Relations and Functions
The document discusses relations and functions. An ordered pair consists of two elements written as (α, β) where order matters. A relation is a set of ordered pairs with a domain (set of first elements) and range (set of second elements). A function is a special relation where each domain element maps to exactly one range element. Several examples demonstrate relations that are and are not functions based on the one-to-one correspondence between domain and range elements.
This document discusses classification techniques in data mining. It defines classification as separating objects into classes either before or after examining the data. The general approach is to decide on classes without looking at data, train the system on a small subset, then use rules derived from attributes to classify the full dataset. Decision trees are constructed by recursively splitting nodes based on attributes that maximize information gain and reduce uncertainty between classes. The document provides an example of building a decision tree to classify animals using attributes like eggs, pouch, flies, and feathers.
The document defines relations and functions. A relation is a set of ordered pairs where the domain is the set of x-values and the range is the set of y-values. A function is a relation where each domain value is paired with exactly one range value. The document provides examples of determining if a relation represents a function using the vertical line test and evaluating functions using function notation.
K TO 12 GRADE 7 LEARNING MODULE IN MATHEMATICS (Q1-Q2)LiGhT ArOhL
The document provides information about sets and set operations including:
1) It defines the complement of a set as the elements in the universal set that are not in the given set.
2) It provides examples of finding the complement of sets and using Venn diagrams to represent complements.
3) It solves a word problem about selecting a student who is not a sophomore by finding the complement of the set of sophomores.
This presentation contains my one day lectures which introduces fuzzy set theory, operations on fuzzy sets, some engineering control applications using Mamdamn model.
Relations are sets of ordered pairs that represent connections between elements. A relation is a function if each element in the domain (input) is uniquely mapped to an element in the range (output). This can be tested using the vertical line test - if a vertical line can pass through the graph of a relation more than once, it is not a function. The domain of a relation is the set of all first elements of each ordered pair, while the range is the set of all second elements. A relation is a function if its domain does not contain repeating elements.
- Normalization is the process of organizing data to avoid redundancy and dependency. It involves organizing the data into tables and establishing relationships between those tables.
- There are various normal forms like 1NF, 2NF, 3NF, BCNF, 4NF and 5NF which represent increasing levels of normalization. As the normal form number increases, the table becomes less prone to modification issues.
- The presentation discusses various concepts related to normalization including functional dependencies, candidate keys, closure, anomalies, and provides examples to explain the different normal forms and when a table satisfies a particular normal form.
Folding Unfolded - Polyglot FP for Fun and Profit - Haskell and Scala - Part 5Philip Schwarz
(download for best quality slides) Gain a deeper understanding of why right folds over very large and infinite lists are sometimes possible in Haskell.
See how lazy evaluation and function strictness affect left and right folds in Haskell.
Learn when an ordinary left fold results in a space leak and how to avoid it using a strict left fold.
Errata:
slide 15: "as sharing is required" should be "as sharing is not required"
slide 43: 𝑠𝑓𝑜𝑙𝑑𝑙 (⊕) 𝑎 should be 𝑠𝑓𝑜𝑙𝑑𝑙 (⊕) 𝑒
Folding Unfolded - Polyglot FP for Fun and Profit - Haskell and Scala - Part ...Philip Schwarz
(download for best quality slides) Gain a deeper understanding of why right folds over very large and infinite lists are sometimes possible in Haskell.
See how lazy evaluation and function strictness affect left and right folds in Haskell.
Learn when an ordinary left fold results in a space leak and how to avoid it using a strict left fold.
This version eliminates some minor imperfections and corrects the following two errors:
slide 15: "as sharing is required" should be "as sharing is not required"
slide 43: 푠푓표푙푑푙 (⊕) 푎 should be 푠푓표푙푑푙 (⊕) 푒
The objective of this paper is to introduce a fuzzy linear programming problem with hexagonal fuzzy
numbers. Here the parameters are hexagonal fuzzy numbers and Simplex method is used to arrive an
optimal solution by a new method compared to the earlier existing method. This procedure is illustrated
with numerical example. This will further help the decision makers to come out with a feasible alternatives
with better economical viability.
Here are examples of the Associative Property and Commutative Property:
Associative Property:
Addition: (2 + 3) + 5 = 2 + (3 + 5)
Multiplication: 3 × (4 × 2) = (3 × 4) × 2
Commutative Property:
Addition: 2 + 5 = 5 + 2
Multiplication: 3 × 4 = 4 × 3
The Associative Property shows that changing the grouping of numbers or variables does not change the sum or product. The Commutative Property shows that changing the order of numbers or variables does not change the sum or product.
Fuzzy logic provides a means of calculating intermediate values between absolute true and absolute false. It allows partial set membership and handles imprecise data. Fuzzy logic systems use membership functions to determine the degree to which inputs belong to sets and fuzzy inference systems to map inputs to outputs. Fuzzy logic has applications in devices like washing machines and cameras that require handling imprecise variables.
This document provides an introduction to fuzzy logic and fuzzy sets. It discusses key concepts such as fuzzy sets having degrees of membership between 0 and 1 rather than binary membership, and fuzzy logic allowing for varying degrees of truth. Examples are given of fuzzy sets representing partially full tumblers and desirable cities to live in. Characteristics of fuzzy sets such as support, crossover points, and logical operations like union and intersection are defined. Applications mentioned include vehicle control systems and appliance control using fuzzy logic to handle imprecise and ambiguous inputs.
The document discusses identifying the domain and range of functions. The domain is the set of all x-coordinates in a relation, while the range is the set of all y-coordinates. A relation is a function if each element in the domain is mapped to only one element in the range - in other words, if each x-value has a single, unique y-value. The document provides examples of stating the domain and range of relations and determining whether they represent functions.
This document defines relations and functions in mathematics. A relation is a set of ordered pairs where the domain is the set of all x values and the range is the set of all y values. A function assigns each element in the domain (set of x values) to exactly one element in the range (set of y values). Functions are commonly represented by letters like f(x), where f denotes the name of the function and x is the variable. The left side of a function equation tells us the name and variable of the function, not that the function is being multiplied.
11.a new computational methodology to find appropriateAlexander Decker
This document proposes a new computational methodology for finding appropriate solutions to fuzzy equations of the form A=B, where A and B are known continuous triangular fuzzy numbers and X is an unknown fuzzy number. It introduces definitions of "positive fuzzy number," "negative fuzzy number," and "half-positive and half-negative fuzzy number." Several propositions and theorems are presented along with proofs to show that the solution to such a fuzzy equation can be a positive, negative, or half-positive/half-negative fuzzy number, depending on the values of A and B. Examples are provided to illustrate solving equations where A and B are positive, negative, or half-positive/half-negative fuzzy numbers. The methodology aims to overcome limitations
A new computational methodology to find appropriateAlexander Decker
This document proposes a new computational methodology for finding appropriate solutions to fuzzy equations of the form A=B, where A and B are known fuzzy numbers and X is an unknown fuzzy number. It introduces definitions of positive, negative, and half-positive/half-negative fuzzy numbers. Propositions and theorems are presented to show that the solution to such an equation can be a positive, negative, or half-positive/half-negative fuzzy number depending on the properties of A and B. Examples are provided to illustrate solving equations where A and B are positive, negative, or half-positive/half-negative fuzzy numbers. The methodology aims to overcome limitations in solving equations where X is an unknown fuzzy number.
The document discusses relations and functions. It provides examples of relations that are and are not functions using ordered pairs. A relation is a function if each element in the domain is mapped to exactly one element in the range. This is determined using a mapping diagram or by applying the vertical line test to a graphical representation of the relation.
The document defines functions and discusses:
- Functions are sets of ordered pairs with each first element paired to a unique second element.
- Functions can be one-to-one or many-to-one.
- Functions are represented in set notation, tabular form, as equations, and as graphs.
- The domain of a function is the set of first elements and the range is the set of second elements.
This document provides an overview of key concepts in algebra including:
- Evaluating algebraic expressions and using variables, formulas, and mathematical models.
- Foundational concepts of sets such as intersections, unions, and subsets of real numbers.
- Properties and applications of real numbers including the number line, inequalities, absolute value, and distance.
- Simplifying algebraic expressions by combining like terms.
Relations and Functions
The document discusses relations and functions. An ordered pair consists of two elements written as (α, β) where order matters. A relation is a set of ordered pairs with a domain (set of first elements) and range (set of second elements). A function is a special relation where each domain element maps to exactly one range element. Several examples demonstrate relations that are and are not functions based on the one-to-one correspondence between domain and range elements.
This document discusses classification techniques in data mining. It defines classification as separating objects into classes either before or after examining the data. The general approach is to decide on classes without looking at data, train the system on a small subset, then use rules derived from attributes to classify the full dataset. Decision trees are constructed by recursively splitting nodes based on attributes that maximize information gain and reduce uncertainty between classes. The document provides an example of building a decision tree to classify animals using attributes like eggs, pouch, flies, and feathers.
The document defines relations and functions. A relation is a set of ordered pairs where the domain is the set of x-values and the range is the set of y-values. A function is a relation where each domain value is paired with exactly one range value. The document provides examples of determining if a relation represents a function using the vertical line test and evaluating functions using function notation.
K TO 12 GRADE 7 LEARNING MODULE IN MATHEMATICS (Q1-Q2)LiGhT ArOhL
The document provides information about sets and set operations including:
1) It defines the complement of a set as the elements in the universal set that are not in the given set.
2) It provides examples of finding the complement of sets and using Venn diagrams to represent complements.
3) It solves a word problem about selecting a student who is not a sophomore by finding the complement of the set of sophomores.
This presentation contains my one day lectures which introduces fuzzy set theory, operations on fuzzy sets, some engineering control applications using Mamdamn model.
Relations are sets of ordered pairs that represent connections between elements. A relation is a function if each element in the domain (input) is uniquely mapped to an element in the range (output). This can be tested using the vertical line test - if a vertical line can pass through the graph of a relation more than once, it is not a function. The domain of a relation is the set of all first elements of each ordered pair, while the range is the set of all second elements. A relation is a function if its domain does not contain repeating elements.
- Normalization is the process of organizing data to avoid redundancy and dependency. It involves organizing the data into tables and establishing relationships between those tables.
- There are various normal forms like 1NF, 2NF, 3NF, BCNF, 4NF and 5NF which represent increasing levels of normalization. As the normal form number increases, the table becomes less prone to modification issues.
- The presentation discusses various concepts related to normalization including functional dependencies, candidate keys, closure, anomalies, and provides examples to explain the different normal forms and when a table satisfies a particular normal form.
Folding Unfolded - Polyglot FP for Fun and Profit - Haskell and Scala - Part 5Philip Schwarz
(download for best quality slides) Gain a deeper understanding of why right folds over very large and infinite lists are sometimes possible in Haskell.
See how lazy evaluation and function strictness affect left and right folds in Haskell.
Learn when an ordinary left fold results in a space leak and how to avoid it using a strict left fold.
Errata:
slide 15: "as sharing is required" should be "as sharing is not required"
slide 43: 𝑠𝑓𝑜𝑙𝑑𝑙 (⊕) 𝑎 should be 𝑠𝑓𝑜𝑙𝑑𝑙 (⊕) 𝑒
Folding Unfolded - Polyglot FP for Fun and Profit - Haskell and Scala - Part ...Philip Schwarz
(download for best quality slides) Gain a deeper understanding of why right folds over very large and infinite lists are sometimes possible in Haskell.
See how lazy evaluation and function strictness affect left and right folds in Haskell.
Learn when an ordinary left fold results in a space leak and how to avoid it using a strict left fold.
This version eliminates some minor imperfections and corrects the following two errors:
slide 15: "as sharing is required" should be "as sharing is not required"
slide 43: 푠푓표푙푑푙 (⊕) 푎 should be 푠푓표푙푑푙 (⊕) 푒
This document discusses techniques for evaluating indefinite integrals using substitution, including pattern recognition, change of variables, and the general power rule. It explains that substitution helps evaluate more complex integrals that involve a composite function. Several examples demonstrate identifying the pattern f(g(x))g'(x) and performing u-substitutions to evaluate the integral. It also discusses the need to sometimes multiply and divide by a constant or perform a formal change of variables if the pattern does not exactly match.
This document discusses techniques for integration using substitution. It explains that substitution allows for the integration of more complex composite functions by breaking them into an inside and outside part. The main techniques are pattern recognition, where the integrand fits the standard pattern of f(g(x))g'(x), and change of variables, where a substitution u is made to simplify the integrand. It provides examples of applying both pattern recognition and change of variables substitutions to evaluate definite and indefinite integrals.
The document defines relations and functions. A relation is a set of ordered pairs, with the domain being the set of all x values and the range being the set of all y values. A function is a special type of relation where each x value is assigned to only one y value. The domain of a function is the set of all valid input values that do not result in illegal operations like division by zero or taking the square root of a negative number.
This document provides an overview and review of key concepts in precalculus that are important for success in Calculus I, including:
- Functions and function notation. Key points are that a function assigns a single output to each input, and function notation (e.g. f(x)) represents the output of a function given a specific input.
- Finding roots of functions by setting the function equal to zero and solving.
- Composition of functions, where the output of one function becomes the input of another. The order of functions in composition matters.
- Other topics like inverse functions, trigonometric functions, exponentials and logarithms are also reviewed at a high level.
The document
Lesson 2 - Functions and their Graphs - NOTES.pptJaysonMagalong
The document provides lesson material on functions and their graphs. It includes sections on defining functions, determining if a relation is a function, functional notation, domain and range, graphing functions, and identifying intervals of increase/decrease. Additional topics covered are relative min/max values, step functions, even and odd functions, and piecewise-defined functions. Examples and exercises are provided to illustrate key concepts.
This document provides examples for representing functions using equations, tables, and graphs. It includes step-by-step worked examples of writing functions to represent real-world situations, making function tables, and identifying whether functions are continuous or discrete based on their graphs. The document also reviews key concepts about functions and their representations that were covered in a previous lesson.
1) The document discusses one-to-one functions and their inverses. It provides examples of determining whether relations are one-to-one and finding the inverses of functions.
2) To find the inverse of a one-to-one function, interchange the x and y variables in the function equation and solve for y in terms of x.
3) The class is divided into groups to practice finding inverses of functions within a time limit and criteria for evaluation.
The document discusses operations that can be performed on functions, including addition, subtraction, multiplication, division, and composition. It defines each operation and provides examples of how to find the sum, difference, product, quotient, and composite of functions. The domain of operations on functions is also discussed.
The document defines relations and functions. A relation is a set of ordered pairs where each element in the domain (set of x-values) is paired with an element in the range (set of y-values). A function is a special type of relation where each element of the domain is mapped to exactly one element in the range. The document provides examples of relations that are and are not functions based on this one-to-one mapping property. It also discusses using function notation and evaluating functions for different inputs. Finally, it explains how to determine the domain of a function by identifying values that would result in illegal operations like division by zero.
A relation is a set of ordered pairs where the domain is the set of all first elements and the range is the set of all second elements. A function is a special type of relation where each element of the domain is mapped to exactly one element of the range. When finding the domain of a function, valid inputs are any values that do not result in division by zero or taking the square root of a negative number.
The document defines key concepts relating to functions and relations:
- A relation is a set of ordered pairs where the domain is the set of all x-values and the range is the set of all y-values.
- A function is a special type of relation where each x-value is assigned to exactly one y-value.
- Function notation uses f(x) to represent the output of a function f when the input is x.
- The domain of a function is the set of all valid input values that do not result in undefined outputs like division by zero or square roots of negative numbers.
The document outlines a lesson plan on determining the inverse of one-to-one functions. The objectives are for students to understand inverse functions and apply them to solve real-life problems. The content covers defining the inverse of a one-to-one function, determining the inverse by interchanging variables and solving for y in terms of x. Examples of finding specific inverses are provided. The lesson concludes with an evaluation where students find the inverses of several functions.
1. The document discusses logarithmic functions, including graphing logarithmic functions, determining their domain and range, and finding intercepts, zeros, and asymptotes.
2. It provides an example of graphing the function y = log2x and discusses key features of logarithmic graphs like being defined only for positive x-values and having a vertical asymptote at x = 0.
3. Determining the domain of a logarithmic function involves setting the argument greater than 0 and solving the inequality to find the domain interval. The range of a logarithmic function is all real numbers.
Here are the answers to the drill questions:
1. y = log2 X ; if x = 2
Given: x = 2
To find: y
Using the definition of logarithm: logb x is the power to which the base b must be raised to produce the value x.
Since 2 = 20, y = 0
2. y = log1/2 X
Given: No value of x is given
To find: y
Using the definition of logarithm: logb x is the power to which the base b must be raised to produce the value x.
Since the base is 1/2, which is less than 1, there is no value of x that can satisfy this
1. This lesson discusses solving real-life problems involving functions. Functions are used to model relationships between quantities in real-life situations where one quantity depends on another.
2. Key skills needed to solve problems involving functions include carefully reading problems, analyzing what is given and required, representing situations as functions, and performing operations on functions to evaluate them.
3. Examples of real-life situations that can be modeled by functions include how virus infections increase over time or transportation fares that vary based on distance traveled. Being able to determine the appropriate function and solve for unknown values allows predicting outcomes.
This document provides an overview of Bloom's Taxonomy, which classifies learning objectives into six levels: Knowledge, Comprehension, Application, Analysis, Synthesis, and Evaluation. Each level is defined and examples of learning objectives for that level are given. The document also discusses using Bloom's Taxonomy to design classroom lectures and assessments that target different cognitive abilities.
Similar to Bco 121 ethics in business (4 ects) case study & rubrics t (20)
A brief description of your employment historyYour career .docxsodhi3
A brief description of your employment history
Your career goals (both short and long term)
Tell me about a leader you look up to. This can be someone you know or don't know, famous or familiar to you, and can even be a TV/Movie character and does not need to real. Describe what this person does makes them your role model.
(My name is Danny Z. i'm a full time student )
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A budget is a plan expressed in dollar amounts that acts as a road map to carry out an organization’s objectives, strategies and assumptions. There are different types of budgets that healthcare organization use to manage its financial and managerial goals and obligations.
Discuss the difference between an operating budget and a capital budget. What are the steps in creating each budget?
At least 150 words; APA Format
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A 72-year-old male with a past medical history for hypertension, con.docxsodhi3
A 72-year-old male with a past medical history for hypertension, congestive heart failure, chronic back pain, and diabetes is admitted to the hospital for hypotension suspected from a possible accidental overdose. What are the criteria for discharge? Explain the importance of utilizating hospital recommendations and teachings. List some meaningful community resources in the response.
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Code of Ethics: This is a synopsis of some of the most important ethical
considerations you need to be aware of as a professional in the real estate
industry.
Terminology:
Agency: The fiduciary relationship created between a principal and an agent whereby the agent
can act on behalf of the principle for certain transactions. Agency is usually created when the
principal signs a listing agreement to list their property for sale or a management contract to rent
a property for instance.
Agent: The broker or sales associate acting on behalf of the principal (see Agency)
Client: The person with whom the broker or sales associate has a legal contract to represent.
Customer: Is not contractually bound to the industry professional
Principal: Person who hires an agent to act on his or behalf.
Code of Ethics:
#1: The agent has a responsibility to promote the interests of their client(s) and treat all involved
in any real estate transaction in an honest and fair manner. They must disclose if they are a
dual agent (representing both buyer and seller in a transaction) or a designated agent
(represent either the buyer or seller depending on state law), or they are a limited representative
(will provide only certain duties in the transaction per state law).
#2: Agents must openly acknowledge to clients any personal interest they might have in any
transaction prior to showing a property; they must acknowledge any personal relationships
involved. Ex: Agent says, “I want to disclose to you before we look at it, that this property
belongs to is my brother and my sister in-law is his agent.”
#3: The Agent will not allow anyone that is not pre-authorized by the owner, to access the
property of the client.
#4: Never overstate benefits or attributes of a property or opportun.
a brief explanation of the effect of Apartheid in South Africa. Prov.docxsodhi3
a brief explanation of the effect of Apartheid in South Africa. Provide two specific examples that demonstrate how people adapted. Finally explain the impact and implications of the changes we have seen in recent years. Cite specific cases. Your original post must be no less than 600 words.
.
A 32-year-old female presents to the ED with a chief complaint of fe.docxsodhi3
A 32-year-old female presents to the ED with a chief complaint of fever, chills, nausea, vomiting, and vaginal discharge. She states these symptoms started about 3 days ago, but she thought she had the flu. She has begun to have LLQ pain and notes bilateral lower back pain. She denies dysuria, foul-smelling urine, or frequency. States she is married and has sexual intercourse with her husband. PMH negative.
Labs: CBC-WBC 18, Hgb 16, Hct 44, Plat 325, Neuts & Lymphs, sed rate 46 mm/hr, C-reactive protein 67 mg/L CMP wnl
Vital signs T 103.2 F Pulse 120 Resp 22 and PaO2
99% on room air. Cardio-respiratory exam WNL with the exception of tachycardia but no murmurs, rubs, clicks, or gallops. Abdominal exam + for LLQ pain on deep palpation but no rebound or rigidity. Pelvic exam demonstrates copious foul-smelling green drainage with reddened cervix and + bilateral adenexal tenderness. + chandelier sign. Wet prep in ER + clue cells and gram stain in ER + gram negative diplococci.
Develop a 1- to 2-page case study analysis, examining the patient symptoms presented in the case study. Be sure to address the following as it relates to the case you were assigned (omit section that does not pertain to your case, faculty will give full points for that section).
The sections that you are to omit are for the above case study are: 1. Explain why prostatitis and infection happen. Also explain the causes of systemic reaction, 2. Explain why a patient would need a splenectomy after a diagnosis of ITP, and 3. Explain anemia and the different kinds of anemia (i.e., micro and macrocytic).
In your Case Study Analysis related to the scenario provided, explain the following:
The factors that affect fertility (STDs).
Why inflammatory markers rise in STD/PID.
Why prostatitis and infection happens. Also explain the causes of systemic reaction.
Why a patient would need a splenectomy after a diagnosis of ITP.
Anemia and the different kinds of anemia (i.e., micro and macrocytic).
PLEASE ANSWER IN DETAIL ALL OF THE ABOVE
.
A 4 years old is brought to the clinic by his parents with abdominal.docxsodhi3
A 4 years old is brought to the clinic by his parents with abdominal pain and a poor appetite. His mother states, “He cries when I put him on the toilet.”
1. What other assessment information would you obtain?
2. What interventions may be necessary for this child?
3. What education may be necessary for this child and family?
Your responses must be at least 150 words total.
.
A 19-year-old male complains of burning sometimes, when I pee.”.docxsodhi3
A 19-year-old male complains of “burning sometimes, when I pee.” He is sexually active and denies using any contraceptive method. He denies other symptoms, significant history, or allergies.
From the information provided, list your differential diagnoses in the order of “most likely” to “possible but unlikely.”
.
A 34-year-old trauma victim, the Victor, is unconscious and on a.docxsodhi3
A 34-year-old trauma victim, the Victor, is unconscious and on a ventilator. He was admitted yesterday, and his condition remains critical. His religious affiliation is unknown; however, he has a tattoo of a crucifix.
What can the nurse do to assess and integrate spirituality into Victor’s care? If the family is in another state what can the nurse do to integrate the family into the care?
Your initial post must include a minimum of 300 words and include proper grammar, punctuation, and reference(s).
.
A 27-year-old Vietnamese woman in the delivery room with very st.docxsodhi3
A 27-year-old Vietnamese woman in the delivery room with very strong and closely spaced contractions. The baby was positioned a little high and there was some discussion of a possible c- section. Despite her difficulties, she cooperates with the doctor's instructions and labors in silence. The only signs of pain or discomfort were her look of concentration and her white knuckles.
· Should she be offered pain medication when she is not showing a high level of pain? Why or why not?
350 words
APA
.
A 25 year old male presents with chronic sinusitis and allergic .docxsodhi3
A 25 year old male presents with chronic sinusitis and allergic rhinitis.
Define adaptive vs. acquired immunity.
Discuss the genetic predisposition of allergens.
Describe the antigen-antibody response.
What is the pathology of sinusitis?
Expectations
Initial Post of Case Study:
Due: Saturday, 11:59 pm PT
Length: A minimum of 250 words, not including references
Citations: At least one high-level scholarly reference in APA from within the last 5 years
Peer Responses:
Due: Monday, 11:59 pm PT
Number: A Minimum of 2 to Peer Posts, at least one on a different day than the main post
Length: A minimum of 150 words per post, not including references
Citations: At least one high-level scholarly reference in APA per post from within the last 5 years
Discussion: Respond to Posts in Your Own Thread
.
A 500-700 word APA formatted PaperInclude 2 sources on your re.docxsodhi3
A 500-700 word APA formatted Paper
Include 2 sources on your reference page in addition to your textbook "
We the People
."
Select one issue area: CIVIL RIGHTS
Research which interest groups represent your issue area
Examine the membership and benefits of groups
Provide data on how much groups contribute to politicians
Discuss legislation the groups helped influence
Include reference page
Submit
your summary in APA format clicking on the assignment in Canvas and uploading your document. Be sure whichever assignment version you choose has an introduction, clear focus, conclusion, and references. Include a reference page for the video clip if that’s what you decide to prepare.
.
A 65-year-old obese African American male patient presents to his HC.docxsodhi3
A 65-year-old obese African American male patient presents to his HCP with crampy left lower quadrant pain, constipation, and fevers to 101˚ F. He has had multiple episodes like this one over the past 15 years and they always responded to bowel rest and oral antibiotics. He has refused to have the recommended colonoscopy even with his history of chronic inflammatory bowel disease (diverticulitis), sedentary lifestyle, and diet lacking in fiber. His paternal grandfather died of colon cancer back in the 1950s as well. He finally underwent colonoscopy after his acute diverticulitis resolved. Colonoscopy revealed multiple polyps that were retrieved, and the pathology was positive for adenocarcinoma of the colon.
Develop a 1- to 2-page case study analysis in which you:
Explain why you think the patient presented the symptoms described.
Identify the genes that may be associated with the development of the disease.
Explain the process of immunosuppression and the effect it has on body systems.
.
A 5-year-old male is brought to the primary care clinic by his m.docxsodhi3
A 5-year-old male is brought to the primary care clinic by his mother with a chief complaint of bilateral ear pain with acute onset that began “yesterday.” The mother states that the child has been crying frequently due to the pain. Ibuprofen has provided minimal relief. This morning, the child refused breakfast and appeared to be “getting worse.”
Vital signs at the clinic reveal HR 110 bpm, 28 respiratory rate, and tympanic temperature of 103.2 degrees F. Weight is 40.5 lbs. The mother reports no known allergies. The child has not been on antibiotics for the last year. The child does not have history of OM. The child is otherwise healthy without any other known health problems.
Physical examination reveals: Vital signsl HR 110 bpm, 28 respiratory rate, and tympanic temperature of 103.2 degrees F. Weight is 40.5 lbs. Bilateral TMs are bulging with severe erythematous. Pneumatic otoscopy reveals absent mobility. Ear canals are nomal.
After your questioning and examination, you diagnose this child with bilateral Acute Otitis Media.
.
92 S C I E N T I F I C A M E R I C A N R e p r i n t e d f r.docxsodhi3
92 S C I E N T I F I C A M E R I C A N R e p r i n t e d f r o m t h e O c t o b e r 1 9 9 4 i s s u e
ome creators announce their inventions with grand
éclat. God proclaimed, “Fiat lux,” and then flooded
his new universe with brightness. Others bring forth
great discoveries in a modest guise, as did Charles
Darwin in defining his new mechanism of evolu-
tionary causality in 1859: “I have called this principle, by which
each slight variation, if useful, is preserved, by the term Natur-
al Selection.”
Natural selection is an immensely powerful yet beautifully
simple theory that has held up remarkably well, under intense
and unrelenting scrutiny and testing, for 135 years. In essence,
natural selection locates the mechanism of evolutionary change
in a “struggle” among organisms for reproductive success, lead-
ing to improved fit of populations to changing environments.
(Struggle is often a metaphorical description and need not be
viewed as overt combat, guns blazing. Tactics for reproductive
success include a variety of nonmartial activities such as earlier
and more frequent mating or better cooperation with partners
in raising offspring.) Natural selection is therefore a principle of
local adaptation, not of general advance or progress.
Yet powerful though the principle may be, natural selection
is not the only cause of evolutionary change (and may, in many
cases, be overshadowed by other forces). This point needs em-
phasis because the standard misapplication of evolutionary the-
ory assumes that biological explanation may be equated with
devising accounts, often speculative and conjectural in practice,
about the adaptive value of any given feature in its original en-
vironment (human aggression as good for hunting, music and
religion as good for tribal cohesion, for example). Darwin him-
self strongly emphasized the multifactorial nature of evolu-
tionary change and warned against too exclusive a reliance on
natural selection, by placing the following statement in a max-
imally conspicuous place at the very end of his introduction: “I
am convinced that Natural Selection has been the most impor-
tant, but not the exclusive, means of modification.”
Reality versus Conceit
N A T U R A L S E L E C T I O N is not fully sufficient to explain evo-
lutionary change for two major reasons. First, many other caus-
es are powerful, particularly at levels of biological organization
both above and below the traditional Darwinian focus on or-
ganisms and their struggles for reproductive success. At the low-
est level of substitution in individual base pairs of DNA, change
is often effectively neutral and therefore random. At higher lev-
els, involving entire species or faunas, punctuated equilibrium
can produce evolutionary trends by selection of species based
on their rates of origin and extirpation, whereas mass extinc-
tions wipe out substantial parts of biotas for reasons unrelat-
ed to adaptive struggles of constituent species in “normal”
t.
a 100 words to respond to each question. Please be sure to add a que.docxsodhi3
a 100 words to respond to each question. Please be sure to add a question and answer a fellow student's question.
Q1. Mead argues that most human understanding of the "self" of animals is fallacious. What is his argument, please explain.
Q2. What does Lacan mean by the subject's assumption of the imago in the short excerpt from the Mirror Stage?
.
A 12,000 word final dissertation for Masters in Education project. .docxsodhi3
A 12,000 word final dissertation for Master's in Education project. A UK L7 writing.
Submitting the dissertation
The dissertation will be submitted online via
blackboard.
Presentation Style
Your research project needs to be clearly presented:
·
The front page should include your
name, project title (around 15 words), your supervisor’s name, the date it
was completed;
·
Work should be presented single
sided, in Arial, minimum font size 11 and be one and a half spaced;
·
A contents page detailing the section
and any tables/charts should be included;
·
Any quotes of less than 12 words
should be identified by quotation marks and kept as part of the paragraph text;
·
Quotes of 12 words and above should
be separated out from the text, indented on the left and right and be displayed
in italics (no quotation marks required);
·
All tables and charts should be
numbered appropriately and have a title;
·
Each section of your project should
be started on a new page;
·
All pages should be numbered;
·
Each section should be numbered (e.g.
1. Introduction) and any charts/graphs within the section should be numbered
accordingly. For example if you are writing about something in section 4.1 (the
first sub-section) then the first chart or graph would be 4.11. So charts and
graphs (if included) are numbered according to the section/sub-section.
Word limit
The project should be written up in
no more than 12,000
words
. This includes everything except the reference list, any appendices
and acknowledgements.
A
final checklist:
1.
Does
your abstract say succinctly what the project set out to do and what has been
found?
2.
Does
your contents page signpost chapter subheadings as well as chapter headings?
3.
Has
your introduction made clear the sub questions/objectives you are addressing in
this enquiry
4.
Is
a framework presented in your lit review chapter and a methodological approach
presented in your methodology chapter, and is it clear how this framework and
methodology inform your data collection, presentation of findings and
discussion and reflections? Have you discussed your positionality?
5.
Does
your discussion chapter relate closely to the data in your results chapter and
tie back to the literature in your literature review?
6.
Have
you answered your research questions?
7.
Have
you carefully considered any ethical implications of your research?
8.
Have
you included a signed, anonymised ethics form in the appendix?
9.
Does
your conclusion summarise what has been found out about the questions you set
yourself in your introduction?
10.
Have you kept to the 12,000 word
limit?
11.
Have you met
all
the assessment criteria?
M
odule
Bibliogr
a
p
h
y
Compulsory
reading:
B
r
y
m
an
,
A
.
(
20
1
6
)
.
S
o
ci
a
l
r
e
s
ea
r
ch
m
e
t
h
o
d
s
(
5
t
h
e
d
.
)
.O
x
f
o
rd
:
O
x
f
o
r
d
U
n
i
v
e
r
sity
P
r
e
ss.
Further optional reading
:
A
l
de
r
s
o
n
,
P
.
&
M
o
rr
o
w
,
V
.
(2
011
)
.
T
h
.
9/18/19
1
ISMM1-UC 752:
SYSTEMS ANALYSIS
Fall 2019 – Lecture 3
Instructor: Dr. Antonios Saravanos
Incremental Model
• Development and delivery of
functionality occurs in increments
• Works well when requirements are
known beforehand
• Projects are broken down into sub-
projects
Source: Project Management for IT-Related Projects (p.
18)
2
9/18/19
2
Incremental Cycle
Incremental Model
9/18/19
3
Iterative Model
• Ideal for situations where not all requirements are
known up front
• Need for development to begin as soon as possible
Source: Project Management for IT-Related Projects (p. 19)
5
Iterative Cycle
9/18/19
4
Iterative Model
Incremental vs. Iterative
• Incremental fundamentally means
add onto. Incremental development
helps you improve your process.
• Iterative fundamentally means re-
do. Iterative development helps you
improve your product.
9/18/19
5
• Is iterative and incremental the
same thing?
Incremental vs. Iterative
Source: http://www.applitude.se/images/inc_vs_ite.png
10
9/18/19
6
Iterative and Incremental Combined
A Simple Software Development Method
• Initial Planning
• Design
• Implementation
• Testing
Source: Making Things Happen: Mastering Project Management (p. 30)
12
n
9/18/19
7
Alistair Cockburn
• What’s Alistair’s take on Iterative vs. Incremental?
Incremental vs. Iterative
• in incremental development, you do each of those
activities multiple times … that is, you go around the
requirements – design – programming – testing –
integration – delivery cycle multiple times. You
“iterate” through that cycle multiple times. (“iterate” –
get it? sigh…)
• in iterative development, you also do each of those
activities multiple times … you go around the
requirements – design – programming – testing –
integration – delivery cycle multiple times. You
“iterate” through that cycle multiple times. By Gummy!
Both of those are “iterative” development! WOW!
9/18/19
8
Incremental vs. Iterative (cont’d)
• Of course, the $200,000 question is,
do you repeat the cycle “on the same
part of the system you just got done
with” or “on a new part of the
system”? How you answer that
question yields very different results
on what happens next on your
project.
Roles
• Product Owner (Business)
– Represents the customer
– Controls the product backlog
– Signs off on deliverables
• The Scrum Master
– Ensures scrum values are understood and kept
– Tracks progress and finds ways to overcome obstacles
• The Development Team
– The people actually responsible for delivering the system
– Self-organizing unit
– Members of the team are generalists not specialists
• Cross functional (Each member of the team knows all aspects of the
product that is being developed)
16
9/18/19
9
The Agile System Development Methodology
17
Manifesto for Agile Software Development
18
9/18/19
10
Manifesto for Agile Software Development
Source: http://www.applitude.se/images/inc_vs_i.
96 Young Scholars in WritingFeminist Figures or Damsel.docxsodhi3
96 | Young Scholars in Writing
Feminist Figures or Damsels in Distress?
The Media’s Gendered Misrepresentation
of Disney Princesses
Isabelle Gill | University of Central Florida
A gender bias seems to exist when discussing Disney princesses in entertainment media that could have
significant consequences for girls who admire these heroines. Prior research and my own extensions have
shown that modern princesses display almost equal amounts of masculine and feminine qualities; how-
ever, my research on film reviews shows an inaccurate representation of these qualities. These media
perpetuate sexist ideals for women in society by including traditionally feminine vocabulary, degrading
physical descriptions, and inaccuracies about the films, as well as syntax and critiques that trivialize the
heroines’ accomplishments and suggest the characters are not empowered enough. The reviews also
encourage unhealthy competition between the princesses and devote significantly more words to these
negative trends than to positive discussions. These patterns result in the depiction of the princesses as
more stereotypically feminine and weak than is indicated by the films themselves, which hinders the cre-
ation of role models for girls.
Despite significant strides women have made
toward combatting sexism in American
society, news and entertainment media rep-
resentations of women continue to be one of
the many obstacles left before reaching
equality. Numerous studies have identified
gender bias in the ways media represent
women (Fink and Kensicki; Niven and
Zilber; Shacar; Wood). Media tend to favor
representations of women who are “tradi-
tionally feminine” as well as not “too able,
too powerful, or too confident,” over more
complex representations (Wood 33). For
example, research by Janet Fink and Linda
Jean Kensicki shows that when media aimed
at both men and women discuss female ath-
letes, their focus is on sex appeal, fashion,
and family rather than athletic accomplish-
ment. Female scientists as well as female
members of Congress also fall victim to this
trend. Interviews with male scientists often
portray them as primarily professionals
while interviews with female scientists tend
to reference their professionalism while high-
lighting domesticity and family life (Shacar).
Similarly, media descriptions of the female
members of Congress focus on domestic
issues even though the congresswomen por-
tray themselves as having diverse interests
(Niven and Zilber). In sum, biased, gendered
representations of women are common in
various forms of media.
Media misrepresentation of women in
these ways can lead to significant social
consequences, such as reinforcing anti-
quated gender roles and diminishing the
perception of women’s impact on society
(England, Descartes, and Collier-Meek;
Fink and Kensicki; Graves; Niven and
Zilber; Shacar; Wood). Since media are
Gill | 97
Gill | 97
likely one of the most p.
Level 3 NCEA - NZ: A Nation In the Making 1872 - 1900 SML.pptHenry Hollis
The History of NZ 1870-1900.
Making of a Nation.
From the NZ Wars to Liberals,
Richard Seddon, George Grey,
Social Laboratory, New Zealand,
Confiscations, Kotahitanga, Kingitanga, Parliament, Suffrage, Repudiation, Economic Change, Agriculture, Gold Mining, Timber, Flax, Sheep, Dairying,
Elevate Your Nonprofit's Online Presence_ A Guide to Effective SEO Strategies...TechSoup
Whether you're new to SEO or looking to refine your existing strategies, this webinar will provide you with actionable insights and practical tips to elevate your nonprofit's online presence.
THE SACRIFICE HOW PRO-PALESTINE PROTESTS STUDENTS ARE SACRIFICING TO CHANGE T...indexPub
The recent surge in pro-Palestine student activism has prompted significant responses from universities, ranging from negotiations and divestment commitments to increased transparency about investments in companies supporting the war on Gaza. This activism has led to the cessation of student encampments but also highlighted the substantial sacrifices made by students, including academic disruptions and personal risks. The primary drivers of these protests are poor university administration, lack of transparency, and inadequate communication between officials and students. This study examines the profound emotional, psychological, and professional impacts on students engaged in pro-Palestine protests, focusing on Generation Z's (Gen-Z) activism dynamics. This paper explores the significant sacrifices made by these students and even the professors supporting the pro-Palestine movement, with a focus on recent global movements. Through an in-depth analysis of printed and electronic media, the study examines the impacts of these sacrifices on the academic and personal lives of those involved. The paper highlights examples from various universities, demonstrating student activism's long-term and short-term effects, including disciplinary actions, social backlash, and career implications. The researchers also explore the broader implications of student sacrifices. The findings reveal that these sacrifices are driven by a profound commitment to justice and human rights, and are influenced by the increasing availability of information, peer interactions, and personal convictions. The study also discusses the broader implications of this activism, comparing it to historical precedents and assessing its potential to influence policy and public opinion. The emotional and psychological toll on student activists is significant, but their sense of purpose and community support mitigates some of these challenges. However, the researchers call for acknowledging the broader Impact of these sacrifices on the future global movement of FreePalestine.
How to Download & Install Module From the Odoo App Store in Odoo 17Celine George
Custom modules offer the flexibility to extend Odoo's capabilities, address unique requirements, and optimize workflows to align seamlessly with your organization's processes. By leveraging custom modules, businesses can unlock greater efficiency, productivity, and innovation, empowering them to stay competitive in today's dynamic market landscape. In this tutorial, we'll guide you step by step on how to easily download and install modules from the Odoo App Store.
How to Manage Reception Report in Odoo 17Celine George
A business may deal with both sales and purchases occasionally. They buy things from vendors and then sell them to their customers. Such dealings can be confusing at times. Because multiple clients may inquire about the same product at the same time, after purchasing those products, customers must be assigned to them. Odoo has a tool called Reception Report that can be used to complete this assignment. By enabling this, a reception report comes automatically after confirming a receipt, from which we can assign products to orders.
Leveraging Generative AI to Drive Nonprofit InnovationTechSoup
In this webinar, participants learned how to utilize Generative AI to streamline operations and elevate member engagement. Amazon Web Service experts provided a customer specific use cases and dived into low/no-code tools that are quick and easy to deploy through Amazon Web Service (AWS.)
Bco 121 ethics in business (4 ects) case study & rubrics t
1. BCO 121 ETHICS IN BUSINESS (4 ECTS) Case Study &
Rubrics
Task
• individual written task in Harvard style format, cover page,
Table of Contents, text alignment and Reference list
• The student must build a coherent discussion or argument in
essay format, analyzing theories and models. Case studies may
be referred
to when providing examples.
• Students must write in complete sentences and develop
paragraphs. No bullet points are allowed.
• Prepare and Introduction, Body, and Conclusion paragraphs.
• Sources must be used, identified, and properly cited.
• Format: PDF submitted through Turnitin
• Complete the following:
A woman is sexually harassed by a top-level senior executive in
a large company. She sues the company, and during settlement
discussions
she is offered an extremely large monetary settlement. In the
agreement, the woman is required to confirm that the executive
did
nothing wrong, and after the agreement is signed the woman is
2. prohibited from discussing anything about the incident publicly.
Before
the date scheduled to sign the settlement agreement, the
woman's lawyer mentions that she has heard the executive has
done this
before, and the settlement amount is very large because the
company probably had a legal obligation to dismiss the
executive previously.
The company however wants to keep the executive because he is
a big money maker for the company.
1. What are the issues of integrity, ethics and social
responsibility posed in the case study? Identify and clearly
describe all the issues
2. What options does the woman have and what ethical theories
(e.g. utilitarianism, deontology, etc.) can she use to help guide
her
decision making? You may argue more than one theory. Cite
your sources.
3. What additional sources or case studies can you use to
support your idea(s) about what she should do and why? Cite
your sources.
4. What ethical theories can the company use to justify their
decisions? Cite your sources.
Formalities:
• Wordcount: 1000 to 1500 words
3. • Cover, Table of Contents, References and Appendix are
excluded of the total wordcount.
• Font: Arial 11 pts.
• Text alignment: Justified.
• The in-text References and the Bibliography must be in
Harvard’s citation style.
Submission: Week 4 – Via Moodle (Turnitin). Due before 21
February 2021 at 23:59.
Weight: This task is 30% of your total grade for this subject.
It assesses the following learning outcomes:
• Outcome 1: Learn how to identify ethical issues.
• Outcome 2: Learn how to address ethical issues in a corporate
setting.
• Outcome 3: Learn how to use Ethical theories to analyze,
critically assess, and make decisions related to ethical issues.
• Rubrics
Identification
of main Issues/
4. Problems
25%
Identifies and
demonstrates a
sophisticated
understanding of the main
issues / problems in the
case study
Identifies and demonstrates
an accomplished
understanding of most of
the issues/problems.
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some of the issues/problems
in the case study
Does not identify or
demonstrate an acceptable
understanding of the issues/
problems in the case study
Analysis and
Evaluation of
Issues /
Problems
25%
Presents an insightful and
thorough analysis of all
5. identified issues/problems
Presents a thorough analysis
of most of the issues
identified.
Presents a superficial
analysis of some of the
identified issues.
Presents an incomplete
analysis of the identified
issues.
Development
of Ideas
and Opinions
25%
Supports diagnosis and
opinions with strong
arguments and well-
documented evidence;
presents a balanced
and critical view;
interpretation is both
reasonable and
objective. Excellent
use of Harvard style
Supports diagnosis and
opinions with limited
reasoning and evidence;
presents a somewhat one-
6. sided argument;
demonstrates little
engagement with ideas
presented. Good use of
Harvard style
Little action suggested
and/or inappropriate
solutions proposed to
the issues in the case
study. Some use of
Harvard style.
No action suggested and/or
inappropriate solutions
proposed to the issues in the
case study. Failed to use or
incorrect use of Harvard
style
Link to Ethical
Theories and
Additional
Research
25%
Makes appropriate and
powerful connections
between identified issues/
problems and strategic
concepts studied in the
course readings and
lectures; supplements
case study with relevant
7. and thoughtful research
and cites all sources of
information
Makes appropriate but
somewhat vague connections
between identified issues/
problems and concepts
studied in readings and
lectures; demonstrates
limited command of the
analytical tools studied;
supplements case study with
limited research.
Makes inappropriate or little
connection between issues
identified and the concepts
studied in the readings;
supplements case study, if at
all, with incomplete
research and
documentation.
Makes no connection
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and the concepts studied in
the readings; supplements
case study, if at all, with
incomplete research and
documentation.
9. each of these steps and take the output
from f, 3x + 4, and return the input x. If we think of the real -
world reversible two-step process of
first putting on socks then putting on shoes, to reverse the
process, we first take off the shoes, and
then we take off the socks. In much the same way, the function
g should undo the second step of
f first. That is, the function g should
1. subtract 4
2. divide by 3
Following this procedure, we get g(x) = x−4
3
. Let’s check to see if the function g does the job.
If x = 5, then f(5) = 3(5) + 4 = 15 + 4 = 19. Taking the output
19 from f, we substitute it
into g to get g(19) = 19−4
3
= 15
3
= 5, which is our original input to f. To check that g does
the job for all x in the domain of f, we take the generic output
from f, f(x) = 3x + 4, and
substitute that into g. That is, g(f(x)) = g(3x + 4) =
(3x+4)−4
3
= 3x
10. 3
= x, which is our original
input to f. If we carefully examine the arithmetic as we simplify
g(f(x)), we actually see g first
‘undoing’ the addition of 4, and then ‘undoing’ the
multiplication by 3. Not only does g undo
f, but f also undoes g. That is, if we take the output from g, g(x)
= x−4
3
, and put that into
f, we get f(g(x)) = f
(
x−4
3
)
= 3
(
x−4
3
)
+ 4 = (x − 4) + 4 = x. Using the language of function
composition developed in Section 5.1, the statements g(f(x)) = x
and f(g(x)) = x can be written
as (g ◦ f)(x) = x and (f ◦ g)(x) = x, respectively. Abstractly, we
can visualize the relationship
between f and g in the diagram below.
11. f
g
x = g(f(x)) y = f(x)
5.2 Inverse Functions 379
The main idea to get from the diagram is that g takes the
outputs from f and returns them to
their respective inputs, and conversely, f takes outputs from g
and returns them to their respective
inputs. We now have enough background to state the central
definition of the section.
Definition 5.2. Suppose f and g are two functions such that
1. (g ◦f)(x) = x for all x in the domain of f and
2. (f ◦g)(x) = x for all x in the domain of g
then f and g are inverses of each other and the functions f and g
are said to be invertible.
We now formalize the concept that inverse functions exchange
inputs and outputs.
Theorem 5.2. Properties of Inverse Functions: Suppose f and g
are inverse functions.
� The rangea of f is the domain of g and the domain of f is the
range of g
� f(a) = b if and only if g(b) = a
12. � (a,b) is on the graph of f if and only if (b,a) is on the graph of
g
aRecall this is the set of all outputs of a function.
Theorem 5.2 is a consequence of Definition 5.2 and the
Fundamental Graphing Principle for Func-
tions. We note the third property in Theorem 5.2 tells us that
the graphs of inverse functions are
reflections about the line y = x. For a proof of this, see Example
1.1.7 in Section 1.1 and Exercise
72 in Section 2.1. For example, we plot the inverse functions
f(x) = 3x + 4 and g(x) = x−4
3
below.
x
y
y = f(x)
y = g(x)
y = x
−2 −1 1 2
−1
−2
1
2
13. If we abstract one step further, we can express the sentiment in
Definition 5.2 by saying that f and
g are inverses if and only if g ◦f = I1 and f ◦ g = I2 where I1 is
the identity function restricted1
to the domain of f and I2 is the identity function restricted to
the domain of g. In other words,
I1(x) = x for all x in the domain of f and I2(x) = x for all x in
the domain of g. Using this
description of inverses along with the properties of function
composition listed in Theorem 5.1,
we can show that function inverses are unique.2 Suppose g and
h are both inverses of a function
1The identity function I, which was introduced in Section 2.1
and mentioned in Theorem 5.1, has a domain of all
real numbers. Since the domains of f and g may not be all real
numbers, we need the restrictions listed here.
2In other words, invertible functions have exactly one inverse.
380 Further Topics in Functions
f. By Theorem 5.2, the domain of g is equal to the domain of h,
since both are the range of f.
This means the identity function I2 applies both to the domain
of h and the domain of g. Thus
h = h◦I2 = h◦ (f ◦g) = (h◦f) ◦g = I1 ◦g = g, as required.3 We
summarize the discussion of the
last two paragraphs in the following theorem.4
Theorem 5.3. Uniqueness of Inverse Functions and Their Graphs
: Suppose f is an
invertible function.
14. � There is exactly one inverse function for f, denoted f−1 (rea d
f-inverse)
� The graph of y = f−1(x) is the reflection of the graph of y =
f(x) across the line y = x.
The notation f−1 is an unfortunate choice since you’ve been
programmed since Elementary Algebra
to think of this as 1
f
. This is most definitely not the case since, for instance, f(x) =
3x + 4 has as
its inverse f−1(x) = x−4
3
, which is certainly different than 1
f(x)
= 1
3x+4
. Why does this confusing
notation persist? As we mentioned in Section 5.1, the identity
function I is to function composition
what the real number 1 is to real number multiplication. The
choice of notation f−1 alludes to the
property that f−1 ◦f = I1 and f ◦f−1 = I2, in much the same way
as 3−1 · 3 = 1 and 3 · 3−1 = 1.
Let’s turn our attention to the function f(x) = x2. Is f invertible?
A likely candidate for the inverse
is the function g(x) =
√
15. x. Checking the composition yields (g◦f)(x) = g(f(x)) =
√
x2 = |x|, which
is not equal to x for all x in the domain (−∞,∞). For example,
when x = −2, f(−2) = (−2)2 = 4,
but g(4) =
√
4 = 2, which means g failed to return the input −2 from its
output 4. What g did,
however, is match the output 4 to a different input, namely 2,
which satisfies f(2) = 4. This issue
is presented schematically in the picture below.
f
g
x = −2
x = 2
4
We see from the diagram that since both f(−2) and f(2) are 4, it
is impossible to construct a
function which takes 4 back to both x = 2 and x = −2. (By
definition, a function matches a
real number with exactly one other real number.) From a
graphical standpoint, we know that if
3It is an excellent exercise to explain each step in this string of
equalities.
16. 4In the interests of full disclosure, the authors would like to
admit that much of the discussion in the previous
paragraphs could have easily been avoided had we appealed to
the description of a function as a set of ordered pairs.
We make no apology for our discussion from a function
composition standpoint, however, since it exposes the reader
to more abstract ways of thinking of functions and inverses. We
will revisit this concept again in Chapter 8.
5.2 Inverse Functions 381
y = f−1(x) exists, its graph can be obtained by reflecting y = x2
about the line y = x, in accordance
with Theorem 5.3. Doing so produces
(−2, 4) (2, 4)
x
y
−2 −1 1 2
1
2
3
4
5
17. 6
7
y = f(x) = x2
reflect across y = x
−−−−−−−−−−−−−−−→
switch x and y coordinates
(4,−2)
(4, 2)
x
y
1 2 3 4 5 6 7
−2
−1
1
2
y = f−1(x) ?
We see that the line x = 4 intersects the graph of the supposed
inverse twice - meaning the graph
fails the Vertical Line Test, Theorem 1.1, and as such, does not
represent y as a function of x. The
vertical line x = 4 on the graph on the right corresponds to the
horizontal line y = 4 on the graph
18. of y = f(x). The fact that the horizontal line y = 4 intersects the
graph of f twice means two
different inputs, namely x = −2 and x = 2, are matched with the
same output, 4, which is the
cause of all of the trouble. In general, for a function to have an
inverse, different inputs must go to
different outputs, or else we will run into the same problem we
did with f(x) = x2. We give this
property a name.
Definition 5.3. A function f is said to be one-to-one if f matches
different inputs to different
outputs. Equivalently, f is one-to-one if and only if whenever
f(c) = f(d), then c = d.
Graphically, we detect one-to-one functions using the test
below.
Theorem 5.4. The Horizontal Line Test: A function f is one-to-
one if and only if no
horizontal line intersects the graph of f more than once.
We say that the graph of a function passes the Horizontal Line
Test if no horizontal line intersects
the graph more than once; otherwise, we say the graph of the
function fails the Horizontal Line
Test. We have argued that if f is invertible, then f must be one-
to-one, otherwise the graph given
by reflecting the graph of y = f(x) about the line y = x will fail
the Vertical Line Test. It turns
out that being one-to-one is also enough to guarantee
invertibility. To see this, we think of f as
the set of ordered pairs which constitute its graph. If switching
the x- and y-coordinates of the
points results in a function, then f is invertible and we have
found f−1. This is precisely what the
19. Horizontal Line Test does for us: it checks to see whether or not
a set of points describes x as a
function of y. We summarize these results below.
382 Further Topics in Functions
Theorem 5.5. Equivalent Conditions for Invertibility: Suppose f
is a function. The
following statements are equivalent.
� f is invertible
� f is one-to-one
� The graph of f passes the Horizontal Line Test
We put this result to work in the next example.
Example 5.2.1. Determine if the following functions are one-to-
one in two ways: (a) analytically
using Definition 5.3 and (b) graphically using the Horizontal
Line Test.
1. f(x) =
1 − 2x
5
2. g(x) =
2x
1 −x
3. h(x) = x2 − 2x + 4 4. F = {(−1, 1), (0, 2), (2, 1)}
20. Solution
.
1. (a) To determine if f is one-to-one analytically, we assume
f(c) = f(d) and attempt to
deduce that c = d.
f(c) = f(d)
1 − 2c
5
=
1 − 2d
5
1 − 2c = 1 − 2d
−2c = −2d
c = d X
Hence, f is one-to-one.
21. (b) To check if f is one-to-one graphically, we look to see if the
graph of y = f(x) passes the
Horizontal Line Test. We have that f is a non-constant linear
function, which means its
graph is a non-horizontal line. Thus the graph of f passes the
Horizontal Line Test.
2. (a) We begin with the assumption that g(c) = g(d) and try to
show c = d.
g(c) = g(d)
2c
1 − c
=
2d
1 −d
2c(1 −d) = 2d(1 − c)
2c− 2cd = 2d− 2dc
2c = 2d
22. c = d X
We have shown that g is one-to-one.
5.2 Inverse Functions 383
(b) We can graph g using the six step procedure outlined in
Section 4.2. We get the sole
intercept at (0, 0), a vertical asymptote x = 1 and a horizontal
asymptote (which the
graph never crosses) y = −2. We see from that the graph of g
passes the Horizontal
Line Test.
x
y
−2 −1 1 2
−1
−2
24. y = g(x)
3. (a) We begin with h(c) = h(d). As we work our way through
the problem, we encounter a
nonlinear equation. We move the non-zero terms to the left,
leave a 0 on the right and
factor accordingly.
h(c) = h(d)
c2 − 2c + 4 = d2 − 2d + 4
c2 − 2c = d2 − 2d
c2 −d2 − 2c + 2d = 0
(c + d)(c−d) − 2(c−d) = 0
(c−d)((c + d) − 2) = 0 factor by grouping
c−d = 0 or c + d− 2 = 0
c = d or c = 2 −d
We get c = d as one possibility, but we also get the possibility
that c = 2 − d. This
suggests that f may not be one-to-one. Taking d = 0, we get c =
0 or c = 2. With
f(0) = 4 and f(2) = 4, we have produced two different inputs
25. with the same output
meaning f is not one-to-one.
(b) We note that h is a quadratic function and we graph y = h(x)
using the techniques
presented in Section 2.3. The vertex is (1, 3) and the parabola
opens upwards. We see
immediately from the graph that h is not one-to-one, since there
are several horizontal
lines which cross the graph more than once.
4. (a) The function F is given to us as a set of ordered pairs.
The condition F(c) = F(d)
means the outputs from the function (the y-coordinates of the
ordered pairs) are the
same. We see that the points (−1, 1) and (2, 1) are both
elements of F with F(−1) = 1
and F(2) = 1. Since −1 6= 2, we have established that F is not
one-to-one.
(b) Graphically, we see the horizontal line y = 1 crosses the
graph more than once. Hence,
the graph of F fails the Horizontal Line Test.
27. x
y
−2 −1 1 2
1
2
y = F(x)
We have shown that the functions f and g in Example 5.2.1 are
one-to-one. This means they are
invertible, so it is natural to wonder what f−1(x) and g−1(x)
would be. For f(x) = 1−2x
5
, we can
think our way through the inverse since there is only one
occurrence of x. We can track step-by-step
what is done to x and reverse those steps as we did at the
beginning of the chapter. The function
g(x) = 2x
28. 1−x is a bit trickier since x occurs in two places. When one
evaluates g(x) for a specific
value of x, which is first, the 2x or the 1 − x? We can imagine
functions more complicated than
these so we need to develop a general methodology to attack
this problem. Theorem 5.2 tells us
equation y = f−1(x) is equivalent to f(y) = x and this is the basis
of our algorithm.
Steps for finding the Inverse of a One-to-one Function
1. Write y = f(x)
2. Interchange x and y
3. Solve x = f(y) for y to obtain y = f−1(x)
Note that we could have simply written ‘Solve x = f(y) for y’
and be done with it. The act of
interchanging the x and y is there to remind us that we are
finding the inverse function by switching
the inputs and outputs.
Example 5.2.2. Find the inverse of the following one-to-one
29. functions. Check your answers
analytically using function composition and graphically.
1. f(x) =
1 − 2x
5
2. g(x) =
2x
1 −x