Composition and Transformation of Functions

Now, let\’s begin our discussion of composition of functions and finding the inverse of a function:

Computing the composition of two functions (Section 1.6) and computing the inverse of a function (Section 1.8), are two of the most important topics we are covering in this module. These algebraic procedures are important in theory and in practice and are relevant in the study of calculus. This discussion activity will help you to become proficient in these skills.

Choose one of the two options:

Create and post two functions, f(x) and g(x), of the types we have considered so far in this course. Make the functions challenging, but not beyond what is covered in the textbook; avoid very simple examples.
Create and post a function, f(x), again, of a type we have already considered in this course.

In this module, we will investigate how the graph/behavior of a given function changes when a constant is added to it, or multiplied by it, or if we replace the independent variable by the variable plus a constant. These are called transformations of a function and are central to really understanding how functions behave. We will then look at how we can add, subtract, multiply, and divide functions, analogous to how we perform such operations with numbers in arithmetic. This is called combining functions. Next, and somewhat related, is evaluating a function at another function (instead of a specific value of the independent variable). This interesting and important topic is called the composition of functions. As we will see, this naturally leads to the idea of an inverse of a given function, which has direct applications in calculus, and in useful, algebraic real-world applications, too.

Finally, we will consider some various, related topics, such as how to determine certain properties of circles based on the standard form of the circle, and how to calculate the distance and midpoint values between any two pairs of points in the Cartesian coordinate system.

All of these topics help us to understand the nature of functions, which is important in properly modeling real-world phenomena.

Operant conditioning has many uses in our everyday lives. Behavior modification uses mostly operant methods in an attempt to change undesirable behaviors such as bad habits. Similar principles are also used in behavioral therapy for a wide range of psychological disorders. Closer to home, operant conditioning can be used to modify the behavior of children and to train pets. In this exercise, we will look at how an animal can be trained by using reinforcement of desired behavior.

As you complete this exercise, consider the following:

How can the principles of operant conditioning be applied to changing behavior?How does reinforcement contribute to behavior change?
By the end of this activity, you will be able to:

Explain the principles and processes involved in operant conditioning

links in the instructions:

https://pantherfile.uwm.edu/johnchay/www/PL06/OC/OC.html

Write a three to five (3-5) page paper

Due Week 3 and worth 200 points Imagine that you are the vice president of operations at a production or service organization. You have noticed that your organization’s current operations strategy is not supporting the challenges that the organization is presently facing. In order to maintain a competitive edge, you must address these challenges with your Chief Executive Officer immediately.Select an existing production organization. Analyze the organization’s current vision, mission, business strategy, operation strategy, supply chain, total quality management, just-in-time philosophy, forecasting method, statistical technique, facility location, work design, project life cycle, and project management.  You will need this information in order to complete this and subsequent assignments.As you collect the information for Assignment 1 and Assignment 2, remember that in Assignment 3 you must prepare a presentation for your Chief Executive Officer.Write a three to five (3-5) page paper in which you:Your assignment must follow these formatting requirements:The specific course learning outcomes associated with this assignment are:

Relative and Absolute Dating

Observe the block diagrams.  Place events in order of occurrence in the respective places below.  Work from oldest to youngest, bottom to top.  Be sure to note any folds, faults and unconformities and their types.Next, using the data provided, answer the questions on radioisotope dating and determine the age of the rock indicated.  Save your files and attach it.APA format.

Healthcare strategy

 : The mission statement is a significant component of the strategic plan. In a well-written paper, define  and discuss its significance, value, and characteristics. Discuss everything that should or should not be included in a mission statement, and explain why.Then, write a mission statement for the organization you have selected for your portfolio project. You will use this mission statement in this final project.Paper Requirements: Your paper should:

Accounting

 Maple, Inc. manufactures syrup that goes through three processing stages prior to completion.  Information on work in the first department, blending, is given below for August:The company uses the weighted-average method.Instructions: Submit an Excel document, with each tab labeled by item number, which demonstrates the following:Provide your answers in a clearly organized Excel spreadsheet. Check spelling and formatting for readability. Document your sources. Where applicable, written comments must be in accordance with APA format.

Week 5 COM

Watch one episode of a sit-com on TV. Take notes of the nonverbal communication used in the show. Briefly describe the show\’s main characters and their relationships then discuss the specific instances of nonverbal communication used in the episode. Use the various types of nonverbal communication in the Week 5 Materials as a guide. Use specific terms and concepts in your discussion.Good shows to use might be Modern Family, Big Bang Theory, The Office, How I Met Your Mother, Seinfeld, Friends, Fraiser, or any other sit-com past or present.  

Compare and contrast In Cold Blood to another filmed depiction of the true crime genre, whether in feature film or…

Compare and contrast In Cold Blood to another filmed depiction of the true crime genre, whether in feature film or TV series form. Have a debatable, persuasive claim and focus on specific points of comparison, using the Lesson in week 7 to guide your structure. Please consult MLA guidance to see how to cite television and film!Your essays should be in MLA Style and approximately 1625-1950 words, not including the Work(s) Cited page. Meeting the minimum word requirement makes you eligible for a C grade. Meeting the maximum word requirements makes you eligible for an A grade. As with most academic writing, this essay should be written in third person. Please avoid both first person (I, we, our, etc.) and second person (you, your). In the upper left-hand corner of the paper, place your name, the professor’s name, the course name, and the due date for the assignment on consecutive lines. Double space your information from your name onward, and don\’t forget a title. All papers should be in Times New Roman font with 12-point type with one-inch margins all the way around your paper. All paragraph indentations should be indented five spaces (use the tab key) from the left margin. All work is to be left justified. When quoting lines in literature, please research the proper way to cite short stories, plays, or poems. You should use the online APUS library to look for scholarly sources. Be careful that you don’t create a \”cut and paste\” paper of information from your various sources. Your ideas are to be new and freshly constructed. Also, take great care not to plagiarize.