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...

...maximum.
Sec11-3 Q70 On a national tour of a rock band, the demand for T-shirts is given by
p = 15 − 4 ln x,
1 ≤ x ≤ 40
where x is the number of T-shirts (in thousands) that can be sold during a single concert at a price of
$ p. If the shirts cost the band $5 each, how should they be priced in order to maximize the proﬁt per
concert?
2
Solution. Let the cost function of the T-shirts be C(x) = ax. Here we ignore the ﬁxed cost term since
the T-shirts are supposed not to be manufactured by the band itself. They simply need to order a
number of T-shirts that they require. When x = 1, C(1) = a = $5.
The Revenue function R is R(x) = xp = 15x − 4x ln x. The proﬁt function P is
P(x) = R(x) − C(x) = 15x − 4x ln x − 5x = 10x − 4x ln x.
Differentiating P(x) with respect to x gives
P (x) = 6 − 4 ln x.
Put it equal to zero for the extrema, we get
6 = 4 ln x
⇒
x = e1.5 = 4.482 thousands of T-shirts.
The second derivative of P(x) clearly is negative:
P (x) = −4
1
x
< 0.
Thus, 4482 T-shirts have to be sold in order to maximize the proﬁt per concert. Substitute x = 4.482
into the price function, we obtain the price per T-shirt:
15 − 4 ln(4.482) = 9 dollars each.
Sec11-3 Q84 A mathematical model for the average of a group of people learning to type is given
by
N (t ) = 10 + 6 ln t , t ≥ 1
where N (t ) is the number of words per minute typed after t hours of instruction and practice (2...

...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...

...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 +...

...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...

...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....

...CHAPTER 4 : FUNCTIONS AND THEIR GRAPHS
4.1 Definition of Function
A function from one set X to another set Y is a rule that assigns each element in X to one element in Y.
4.1.1 Notation
If f denotes a function from X to Y, we write
4.1.2 Domain and range
X is known as the domain of f and Y the range of f. (Note that domain and range are sets.)
4.1.3 Object and image
If and , then x and y are known respectively as the objects and images of f. We can write
, , .
We can represent a function in its general form, that is
f(x) = y.
Example 4.1
a. Given that , find f(0), f(1) and f(2).
Example 4.2
a. Given that , find the possible values of a such that
(a) f(a) = 4, (b) f(a) = a.
Solution
a. Given that , find f(0), f(1) and f(2).
b. Given that , find the possible values of a such that
(a) f(a) = 4, (b) f(a) = a.
(a)
(b)
4.2 Graphs of Functions
An equation in x and y defines a function y = f(x) if for each value of x there is only one value
of y.
Example:
y = 3x +1, , .
The graph of a function in the x-y plane is the set of all points (x, y) where x is the
domain of f and y is the range of f.
Example
Figure 1 below shows the graph of a linear function, the square root function and a general function.
y = f(x)
y = x...

...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...

...Four Functions of Management
Jennifer Tsouloufas
MGT / 230 Management Theory and Practice
January 14, 2013
Mark Hardee
Abstract
This paper will attempt to define and describe the four functions of management, planning, organizing, leading, and controlling. It will also relate each function to observations within the organization that I work.
Planning
“Management in the process of working with people and resources to accomplish organizational goals” (Bateman, Snell, 2011, para. 1). A good balance of both will produce the most successful and efficient results. Although methods may change with the times, there are fundamentals that remain timelessly effective. The first function of planning is a strategy. Because this first step will lead the others, it is crucial to look at outlying factors that may conflict or affect the organization’s ultimate goal. Most of this information will be drawn from the mission statement of the company (Rothbauer-Wanish, 2009). At this stage, setting objectives, and following up on the execution of the plan are extremely critical.
I work for a large corporation that deals in all fields of apparel, accessories, and home goods. We are briefed quarterly in regard to upper managements “vision plan” for the season. We are usually given the numbers, profit, and loss for the previous season and challenged to improve using our strengths, creativity, and trend knowledge. Because...