1.Logic
∃there exist
∀for all
p⇒q p implies q / if p, then q
p⇔q p if and only if q /p is equivalent to q / p and q are equivalent 2.Sets
x∈A x belongs to A / x is an element (or a member) of A
x∉A x does not belong to A / x is not an element (or a member) of A A⊂B A is contained in B / A is a subset of B
A⊃B A contains B / B is a subset of A
A∩B A cap B / A meet B / A intersection B
A∪B A cup B / A join B / A union B
A\B A minus B / the diference between A and B
A×B A cross B / the cartesian product of A and B
3. Real numbers
x+1 x plus one
x-1 x minus one
x±1 x plus or minus one
xy xy / x multiplied by y
(x-y)(x+y) x minus y, x plus y
= the equals sign
x=5 x equals 5 / x is equal to 5
x≠5 x (is) not equal to 5
x≡y x is equivalent to (or identical with) y
x>y x is greater than y
x≥y x is greater than or equal to y
x<y x is less than y
x≤y x is less than or equal to y
0<x<1 zero is less than x is less than 1
0≤x≤1 zero is less than or equal to x is less than or equal to 1 |x| mod x / modulus x
x2 x squared / x (raised) to the power 2
x3 x cubed
x4 x to the fourth / x to the power 4
xn x to the nth / x to the power n
x (−n) x to the (power) minus n
x的平方根(square) root x / the square root of x
x的三次根cube root (of) x
x的四次根fourth root (of) x
x的n次根nth root (of) x
(x+y)2 x plus y all squared
n! n factorial
x^x hat
x¯ x bar
x˜ x tilde
xi xi / x subscript i / x suffix i / x sub i
∑(i=1~n) ai the sum from i equals one to n ai / the sum as i runs from 1 to n of the ai 4. Linear algebra
‖x‖the norm (or modulus) of x
OA→OA / vector OA
OA¯ OA / the length of the segment OA
AT A transpose / the transpose of A
A−1 A inverse / the inverse of A
5. Functions
f(x) fx / f of x / the function f of x
f:S→T a function f from S to T
x→y x maps to y / x is sent (or mapped) to y
f’(x) f prime x / f dash x / the (first) derivative of f with respect to x f”(x) f double-prime x / f double-dash x / the second derivative of f with...

...Functions and graphing functions
Basics:
A function is a rule that changes input into output
A relation is any set of ordered pairs
A function is defined as a set of ordered pairs in which no two ordered pairs have the same element
A function must give exactly one unique output for each input
Also called a mapping or simply a map
The set of input numbers is called the domain
The set of output numbers is called the range
The set of all possible outputs is called the co-domain
The range is generally the subset of the co-domain however they can also be the same
Brackets:
A domain described as
That is, the square bracket means p is included. The rounded bracket means q is not included.
Number systems:
Composite functions:
When one function is followed by another function, the result is a composite function
Applying function after applying function is written in 3 different ways
All are pronounced ‘ after’ and mean ‘do followed by ’
Examples:
(i) Evaluate
(ii) Evaluate
(iii) Find the values for for which
(iv) Find
The number of people who visit a circus can be modelled by where represents theattendance of the circus days after it opens. The profit made by the circus can be modelled by where represents the profit in euros for the circus on a day when people attend
(i) Find the number of people who...

...BIRONDO EDUCATION SUPPORT TUTORIAL CENTER
MATH IV- CHAPTER 2-1 to 2-3
I. Decide whether the relation is a function. If it is a function, state the domain and range.
1. {(-5, -2), (-1, 1), (3, -6), (8, 1)} 2. {(2, -9), (2, -2), (6, 8), (8, 1), (11, -7)}
3. a x 4.
b y
c z
5. 6.
7. 8. 9.
II. FUNCTION NOTATION. Solve the following:
1. f(x) = x3 – x 2– 6x 2. g (x) =
a. f(-2) – f(9) a. g(5) + g(10)
b. -6 [(f(0) + f(9)] b. 8 [g(1) - g(2)]
III. LINE OF BEST FIT. Identify the following:
Name
No. Of Pencils
No. Of Rulers
Abigail
4
1
Bob
16
4
Frank
7
8
Peter
4
5
James
7
2
Alex
27
14
Jack
4
2
Paul
6
3
Lucie
4
2
Jenna
0
1
Claire
2
1
Kym
4
0
a. Sketch a scatter plot for the data.
b. Find the best fit line.
c. Sketch the best fit line on the scatter plot at the left.
d. Use the best fit line to predict the number of rulers does Paul if he has 30 pencils.
e. Find r.
f. Write a sentence which explains the direction and strength of the correlation.
2. Sand lance fish (found in the Northwest Atlantic) were collected and there age and length were recorded.
Age (years) 2 3 4 5 6 7 8
Mean Length (mm) 176...

...Management:
Four Main Functions of Management
There are four main functions of management; planning, organizing, leading, and controlling. All four functions have a significant role in the maintaining of efficient and effective management.
Planning
The first function of management is planning, which is the management function of systematically making decisions about the goals and activities that the overall organization will pursue, including making decisions for individuals and groups within the organization (Bateman & Snell 16). In the company that I work for, there is little organization. This could be attributed to management as well as the store being only 3 weeks old and everyone just getting the hang of things. I feel that if the management had better planning a lot of the short falls would not have happened. Short falls such as running out of important Christmas items, and not having maps of the store for customers (the maps were a major complaint, many customers would refer to another location that gave out maps). My company is one of the largest retail chains in the world and planning is a must.
Organization
Organization is the process of establishing formal relationships among people and resources in order to reach specific goals and objectives. Organizational structure is represented primarily by an organizational chart. It specifies who is to do what and how it will be...

...night she keeps the movie. Choose the cost function that represents this scenario if x equals the number of nights Laura has the movie.</object:standard:macc.912.f-if.1.2
c(x) = 2.00x + 0.50
c(x) = 2.00 + 0.50x
c(x) = 2.50x
c(x) = (2.00 + 0.50)x
Points earned on this question: 2
Question 4 (Worth 1 points)
(03.02)<object:standard:macc.912.f-if.1.2
If g(x) = x2 + 2, find g(3).</object:standard:macc.912.f-if.1.2
9
8
11
6
Points earned on this question: 1
Question 5 (Worth 1 points)
(03.02)<object:standard:macc.912.f-if.1.3
Generate the first 5 terms of this sequence:
f(1) = 0 and f(2) = 1, f(n) = f(n - 1) + f(n - 2), for n > 2.</object:standard:macc.912.f-if.1.3
0, -1, 1, 0, 2
0, 1, 1, 2, 3
0, 1, 2, 2, 3
0, 1, 1, 2, 2
Points earned on this question: 1
Question 6 (Worth 1 points)
(03.02)<object:standard:macc.912.f-if.1.2
Let f(p) be the average number of days a house stays on the market before being sold for price p in $1,000s. Which statement best describes the meaning of f(250)?</object:standard:macc.912.f-if.1.2
The house sold for $250,000.
The house stayed on the market for an average of 250 days before being sold.
This is the average number of days the house stayed on the market before being sold for $250,000.
The house sold on the market for $250,000 and stayed on the market for an average of 250 days before being sold.
Points earned on this question: 1
Question 7 (Worth 1 points)
(03.02)
For the function f(x) = x +...

...Running head: Functions of Management
Functions of Management
Joan A. Mendiola
MGT330 – Management, Theory, Practice and Application
Milton Wingert
June 20, 2011
Most businesses are guided through some type of philosophy that may increase in profit and to ensure the business success and growth according to (Bateman & Snell 2007). This paper will demonstrate the following four functions of management; planning, organizing, leading and controlling. These types of functions must be performed by the management teams depending on the level of industry, title or the amount of obligations or task within the company. The four types of functions will define the roles and responsibility of each team. This paper will explain those four functions and how they currently apply in my workplace.
First function is planning, this type defines as being able to set some type of goal or deciding the course of action, it is developing rules and regulations, developing plans on both the organizations and people that actually work in it as well as forecasting on what the...

...rather than issuing mandates. Now the leadership and management are defined, we can move on to describe management in terms of its four functions. These functions are identified as planning, organizing, leading, and controlling. How well managers perform these key functions determines whether a business is successful.
Planning, in its simplest form, is establishing organizational goals and objectives and deciding how to accomplish them. It is the primary function, often referred as the "first" management function because all the management functions depend on planning. Managers engage in planning by determining where the firm should be going and how best to get there. Once goals and objectives have been set for the organization, managers must develop plans (or actions) for achieving them. A plan could be defined as an outline of the actions by which the organization intends to accomplish its goals and objectives. The company that I work for, 7-Eleven, I, as a manager, set a goal to sell as many products as possible to increase the sales. I have to ensure that the customer knows about the products we are selling. My number one target is the customer and the way to achieve is through my employees, who can provide the outstanding customer service and thus, the customer will come back.
After goal setting and planning, the second major function of the management is organizing....

...Graphs and Function
What is the relation between the graphs and function and how was it applied in the real world?
Graphs are frequently used in national magazines and newspaper to present information about things such as the world’s busiest airports (O’Hare in China is first, Heathrow in London is sixth), about the advertising-dollar receivers in the United States (newspaper are first, radio is fourth) and about NCAA men’s golf team title winner (Yael is first, Houston is second). The function concept is very closely connected to graphs, and functions are the heart of mathematics.
I gathered my information from books especially algebra books and some are from the internet. I went to the library to look for some books and I borrowed some so I have many resources of information.
Many real-life relations between two quantities expressed in the form of equation are functions. To visualize these relationships, geometric figures called graphs are used. Modern technology provides us with graphing utilities needed to draw these graphs as well as enhance man’s knowledge of graphing techniques. Scientist and astronomers identify, visualize, and explore graphical patterns useful in analyzing data about the universe. Economist and businessmen draw mathematical models to find curves of best fit. Generally, the use of function and graphs is found in every scientist and...

...Transfer Function
General with order, linear, time invariant differential equation
an dn(t)dtn+ an-1 dn-1c(t)dtn-1+…a0ct= bmdmrtdtm+bm-1dm-1rtdtm-1+…b0r(t)
Where: c (t) is the output
r (t) I is the input
By taking the Laplace transform of both sides
ansn cs+ an-1sn-1 cs+…a0cs+initial condition involving c(t)
=bmsmRt+bm-1sm-1Rt+…b0Rs+initial condition involving r(t)
If we assume that all initial condition are zero
ansn+ an-1sn-1….+…a0cs=bmsm+bm-1sm-1+…b0r(s)
Rs-→ bmsm+bm-1sm-1+…b0ansn+ an-1sn-1….+…a0--→c(s)
Gs=c(s)r(s)=bmsm+bm-1sm-1+…b0ansn+ an-1sn-1….+…a0
Transfer function ratio of output over input
Laplace Transfer Theorem
1. L f(t)=Fs=0∞f(t)e-stdt
2. L Kf(t)=KF(s)
3. L f1t+f2t=F1s+F2s superposition theorem
4. L e-atft=Fs+a complex shifting theorem
5. L ft-a=e-as F(s) real shifting theorem
6. L fat= 1aFsa similarity theorem
7. L dfatdt=sFs-f(0) derivative theorem
8. L d2fatdt2=s2Fs-sf'0-f(0)
multiple derivative theorem
9. L 0τfτdτ=F(s)s integral theorem
Example
Find the transfer function represented by
* d(t)dt=2ct=r(t)
Gs=c(s)r(s)
First find the Laplace transform
L d(t)dt+2 L ct=L r(t)
scs+2cs=r(s)
s+2cs=r(s)
c(s)r(s)=1s+2 To find Gt the solve for inverse Laplace transform
Find the transfer function Gs=Y(s)u(s)
L d2Ytdt2+ L dYtdt+ L Yt=2 L dutdt+L ut
s2Ys+sYs+Ys=2s us+u(s)...