Analysis of Functions


Functions are traditionally represented on a two dimensional Cartesian axis. The most familiar version is to have the horizontal axis labeled as x and the vertical axis labeled as a function of x. This paper will analyze some simple functions along with a few manipulations thereof. The following three functions are to be considered:
f(x) = 2x + 5
g(x) = x2 – 3
h(x) = (1/3) * (7 – x).

For the first part, the goal is to determine (f – h) (4). The first step is to find the general form for the difference of the two functions f(x) and h(x):
2x + 5 – ((1/3) * (7 – x))
(1/3) * (6x + 15) – (1/3) * (7 – x)                Rewrite f(x)
(1/3) * (6x + 15 – 7 + x)                                       Factor out (1/3)
(1/3) * (7x + 8)                                           Collect terms
Now substitute 4 in for x:
(1/3) * (28 + 8) = (1/3) * 36 = 12.

For the composition functions, the entire inner function is inserted into the outer function. Consider the following two examples:

f(g(x)) = f(x2 – 3)
= 2(x2 – 3) + 5
= 2x2 – 1

h(g(x)) = h(x2 – 3)
= (1/3) * (7 – (x2 – 3))
= (1/3) * (10 – x2).

Graphing a function is fairly straight forward. For each value of x on the horizontal axis, match it with the function value on the vertical axis. In order to transform the function to the right by 6 units, it is necessary to replace x with x – 6. In order to transform the function downward by seven units, it is necessary to subtract 7 from the value of the function. This gives:
g(x) = x2 – 3
gT(x) = (x – 6)2 – 3 – 7
= (x – 6)2 – 10.
The graph on the following page shows the original function in blue and the transformed function in red.

To find the inverse of a function, simply interchange the function expression and the variable x. For the functions f(x) and h(x) we find:
f(x) = 2x + 5                                      Original function f(x)
x = 2 * f’(x) + 5                       Interchange as described
x – 5 = 2 * f’(x)                       Subtract 5 from both sides
f’(x) = (1/2) * (x – 5)               Divide both sides by 2

h(x) = (1/3) * (7 – x)                Original function h(x)
x = (1/3) * (7 – h’(x))              Interchange as described
3x = 7 – h’(x)                          Multiply both sides by 3
h’(x) = 7 – 3x                          Isolate h’(x)

Presented here are some fairly direct applications for simple functions. While complexity can increase as the functions become more intricate, the process remains the same. Each step above can be a powerful tool for analyzing functions under different circumstances.




Annenberg Learner (2012).  Math in Daily Life, retrieved on December Jan 2,

2014, from:


Ashford University (2012). Student Guide MAT222: Introduction to Algebra.

Retrieved on Jan. 2, 2014, from:


Dugopolski, M. (2012). Elementary and intermediate Algebra (4th Ed.). New

York, NY: McGraw-Hill.

Blogging and individualization

In fame, the article illustrates theoretical discussion of social networking websites, blogs and micro blogs.   The article ascertains that the media phenomena are illustrative and symptomatic of both the larger social-cultural trends and technological affordances. In this way, the article affirms that media links the content of new media products and the current ongoing technological and cultural processes can literally be considered problematic.

Critically, the author has illustrated media phenomena in a more negative way, where he portrays that media is an illustration of technological affordances. Media cannot be technological affordance; rather it is a channel, which those who wish to access can be able to even if he or she cannot afford. The issue is not how a person can afford, but how an individual is willing to use it. In other words, it is criticize-able that; the issue affirmed by the author that new media are illustrative of both larger socio-cultural and technological affordances trends is vague. Without media, people used to socialize, and still they can socialize without it. At the same time, any one can use the media, and not only those who can afford.  Further, the article concludes that media will link the information of two new media, with certain ongoing technological and cultural process, which at the end is termed as problematic. The linking itself is personal. Media is not available to cause problems but rather to show direction. Therefore, cultural and technological processes are only propelled using media and not implemented by it.

According to fame also, the article affirms that internet has become more of an interaction channel, which people use to get information. Further, the users are ”content”, only in the interactive ICTs as well as pervasive communication. The truth is that those who use the internet, are after information, and that they cannot themselves be content as stated in the article. For instance, students usually use the internet to do research. With that, it is clear that those who have the information already with them will not in any way search the internet as they already have what is contained in the internet. Again, the author narrates that there is massive popularity of blogging, micro blogging and social networking on the net, which is true. However, he ascertains that other communication technologies evident the fact that other people and connections to them in the post social world are the ones who are being increasingly consumed.  This is not true as, social networking, blogging and micro blogging, affects directly those people who are in the post social system.

In other words, those people who blog by themselves, and those who interact to form a social network in the internet, will directly be affected, either in positive or negative way depending on the manner in which they use social networks.  Generally, the article demonstrates that currently people have propelled a ‘phatic media’ environment, where communication takes place without content. Which is not true, there is no single way people can communicate without content. The only difference is that content will vary due to issues like age, sex and culture, however the truth is that at the end of the day, content has been passed. Lastly, the article assumes that the movement from blogging to micro-blogging and social networking corresponds to movement from narratives, communities and substantive communication. This is criticize-able also since; social networking is creation of more communities and not moving from communities.




A.  Please use the database you created in the Previous assignment (See snap shot picture below of database). Show your work.




GRANT[READ, Insert, Delete, Update] ON Table Customer TO Public


  1. Create at least two different users and implement their permissions using SQL statements.


GRANT Select ON Table Customer TO User1;

GRANT READ ON Table Customer TO User2;


B. “Consider the following normalized relations for a database in a large retail store chain:


STORE (Store_ID, Region, Manager_ID, Square_Feet)

EMPLOYEE (Employee_ID, Where_Work, Employee_Name,


DEPARTMENT (Department_ID, Manager_ID, Sales_Goal)

SCHEDULE (Department_ID, Employee_ID, Date)









In this case we should use centralized database for this retail store chain. A central computer or system holds the retails data on a central computer whether it is a mainframe or server. Computers and dumb terminals which are on a network can access it and the distance of these terminals of some distance from the central database. We should use the centralized database because it is easier to organize, edit, update and backup the data. Communication also becomes easier if the data is held centrally. This database is easier to manage and control and making of the backup of the data is far easier by using a suitable backup strategy.




A distributed database is a single database which is logically spread across the computers in multiple locations which are communicated by data communication network. The distributed database can be centrally administered while providing flexibility and customization. The network must allows its users to share the data and the user at certain location must be able to access the data in different location. The user may be separated geographically over a large area or over a small area like in a building. Replication and duplication ensure that the distributed system is up to date and current. The computers using this database may range from micro computers to large scale computers. A distributed database requires multiple database management systems running at different sites at different computers. The degree to which these database systems cooperate and whether there is a master which coordinate requests involving data from multiple sites distinguish various types of distributed database environments.

Philosophical Viewpoints on Social Welfare Policies

PART 1: Philosophical Viewpoints on Social Welfare Policies


Social welfare policies in the United States of America were influenced by economic crises, political preferences and wars. In the stream of welfare policies in America, Work Opportunity Reconciliation Act and Personal Responsibility set the course for the social welfare programs by establishing various welfare programs. This involved using federal grants with the objective of promoting self-sufficiency among vulnerable members of the society.  This has however been viewed from different angles by different ideological groupings notably conservatives and liberals.



With regards to social welfare policies, conservatives generally oppose government intervention since they consider it as a waste of tax payer’s money. Social welfare policies are viewed as providing benefits to people who do not require them or it creates a dependency for people by encouraging them to stop caring for themselves. Liberalists on the other hand are actively in support of government intervention. They consider social welfare policies as important and which should be legislated by the government. They argue that welfare policies should not be left to operate freely without controls. Liberal and conservative views are considered contradictory and exclusionary but more often competing.





Segal, E. A. (2010). Social welfare policy and social programs: A values perspective. Australia: Thomson Brooks/Cole.