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

Women in Art: Then & Now

Answer the Following Questions and compare and contrast 5 paintings to answer them.
How has the portrayal of women in art throughout the years shaped women into how they are thought of and portrayed today?
Why is humanities an important concept?
The 5 paintings to be used are:
The Two Fridas
Les Demoiselles d\’Avignon
Olympia by Edouard Manet
Sunday Afternoon on the Island of La Grande Jatte
The Drowning Girl by Roy Lichstein

If possible, please try to fit this into the introduction paragraph:

In Humanities this year, we have studied some of the most famous and influential art, music, literature, culture, fashion and politics of all time. We learned how to define the meanings of the arts through analysis and differentiate each one by time period and style. Humanities is an important concept because it portrays the evolution of humans and natural life through works of the arts and helps modern day people to understand the impressions that people in the olden days had of life.

Any topic (writer\’s choice)

The Annotated Bibliography must include at least five reputable sources, whether those sources come from our Digital Casebook, The Politics of Sports, or somewhere else. Additionally, each of your five annotations must include the following, described on page 243 of the chapter on Canvas:

A correct MLA Works Cited Page Entry for that source.
A Descriptive Annotation summarizing the argument, explaining its main points, and describing the method or structure of the argument.
An Evaluative Annotation (a.k.a. Critical Annotation) reflecting on the sources role in your project, explaining how it adds to your understanding of the QAI, explaining whether it changes your understanding of the conversation, demonstrating how it relates to your other sources and might lead to new sources, etc.

here are the links for five sources: http://www.independent.co.uk/sport/football/news-and-comment/fifa-corruption-scandal-sepp-blatter-reveals-agreement-in-place-for-russia-to-host-2018-world-cup-a6712061.html

https://mic.com/articles/58649/russia-s-anti-gay-law-spelled-out-in-plain-english#.wPyBo4j9v

http://www.independent.co.uk/sport/football/international/russia-2018-racism-guaranteed-at-world-cup-as-incidents-double-a6768701.html

http://edition.cnn.com/2015/07/24/football/world-cup-fifa-russia-racism-football/

http://www.ctvnews.ca/world/attack-on-russian-police-station-raises-world-cup-2018-concerns-1.2853584

Using t-Test

To prepare for this Assignment, review the Required Readings from Triola found in the Learning Resources for this module. Think about how inferential statistics uses sample data to make inferences about population parameters. Also, review A Simple Guide to IBM SPSS Statistics regarding t-tests.
Assignment Guidelines:
Access Module 2 Assignment 1: Using t-Tests, which can be found in the Learning Resources for this module.
Access the dataset in the SPSS program.
Complete the analyses described in Module 2 Assignment 1 by following the directions within the document.
Write a 2-page paper that includes the results found from your analysis and your interpretation of the data. Include the output from the t-tests in your explanation of the results. Follow proper APA format and guidelines for writing and charting.
As an option, use the Peer Help Desk discussion area to give and receive help from your colleagues on using SPSS. This can include attaching screenshots (embedded in a MS Word document), step-by-step directions, or general help in solving the problems.

Any topic (writer\’s choice)

Complete, detailed Goal Achievement Plan for three goals of your choice related to your career development. For each of your goals, include a goal narrative, resources and timeline section. A description of each section is as follows:
Goal Narrative
A statement of your goal
A brief description of the steps you intend to take to accomplish your goal
A description of the specific criteria by which you will measure whether your goal has been achieved
Resources
Your resources section should include three resources with a description of how each is relevant to your goal.
Your resources must include the following:
One reading (book, periodical, journal, etc.)
One Internet resource
Another resource of your choice which may also include:
Attendance at one conference, seminar or presentation
One-on-one informal interview or discussion with a professional in a role that you would be interested in as a graduate
Timeline
A description of each action step and timing for achieving each goal

INVESTIGATION TO DETERMINE THE CAPACITANCE (C) BY MEASURING THE ENERGY STORED IN THE CAPACITOR WITH INCREASING VOLTAGE

Virtual Experiment
For the purpose of this exercise, you are not required to physically perform the experiment. Data will be generated using the virtual simulation on the website indicated below
https://phet.colorado.edu/en/simulation/capacitor-lab

Procedure Task 1
1. Go to the following web address:
https://phet.colorado.edu/en/simulation/capacitor-lab
2. Download the Capacitor Lab and run the simulation
3. Under the Meters tab on the right of the simulation window, select the following
tick boxes:
Stored Energy Voltmeter
4. Drag the red and black measuring probes from the voltmeter so that each probe is connected to a different plate
5. Check that the voltmeter screen reads 0V to begin
6. Carefully change the value of the voltage by adjusting the button shown on the
battery
7. Record the value shown on the voltmeter and the corresponding value of E
shown on the stored energy bar
8. Repeatfor5morepositivevalues,upto1.5V
9. Plot a graph of E and against V2 to find the gradient
10.Given that = ( ) 2, calculate 2
Task 2
Knowing that: = 0
Where: 0 = permittivity of free space = 8.85 1012 = plate separation (distance in mm)
= area of plate (m2)
Calculate the plate separation required for a capacitance of 1.6 1013F and then
compare to the experimentally found value.
1. Under the Meters tab on the right of the simulation window, select the following tick box:
Capacitance
2. Using the same plate area as before (100mm2) as before, adjust the separation until 1.6 1013F is measured

please also look at the attached files there are very important because it will tell exactly how do the experiment online and also the format of the essay

The Transmission Model – Essay

The Sender/Message/Channel/Receiver or Transmission Model is a dated model that is still useful in identifying the players in the mass communication process. Identify one media messages from two different media sources. For example, MSNBC and Fox News (media sources) news report on the same story about Donald Trump (media message). Write a 250-500 word essay describing who the sender is, how the message was encoded, the channel used to send the message, and who received the message. Also discuss how the receiver may decode the message. Submit your observations in a Microsoft Word document.