Excel provides two functions specifically for calculating cumulative interest and principal payments on a loan: CUMIPMT, which calculates the cumulative interest payments of a bond or note and CUMPRINC, which calculates the cumulative principal payments of a bond or note.

Some background information on the Cumulative Interest and principal payments add-in functions

Both functions use the same arguments, including the interest rate, duration) of the loan (or number of periods, the grantBalance (or present value), the start and end dates of the period for which you calculate the cumulative interest or principal payments will, and change a type of pension, to see if the stream of payments that occur as a normal retirement pension or an annuity due.

The interest rate maturity of loans, loan balance, and the kind-of-annuity switch arguments in the same way for the CUMIPMT CUMPRINC functions and how they work for the standard financial functions.

Note: If youQuestions about how the interest rate, loan term, loan balance, or type ofannuity
Switch arguments work, see above in the section "Using the Payment Functions."

The start date and end date for arguments, as mentioned above, enter the start and end points of the period for which you calculate the cumulative interest or principal will be paid.

Common Errors Made in the use of cumulative interest and principal functions

Both the CUMIPMT andCUMPRINC functions return an error value in several predictable situations, and a surprising situation:

1. If the interest rate or loan term is less than or equal to zero.

2. If the beginning or ending date is unreasonable, or if the beginning is the ending
Date.

3. If the loan is net present value is less than or equal to zero. (Note that this means that you do not use
to show the convention of indicating present value of the loan as a negative number,that
it is a cash outflow.)

With the function CUMIPMT

The CUMIPMT function calculates the cumulative interest paid on a loan between two dates you specify as changing the interest rate, credit, credit cash value, start and end dates and the type-of-retirement. It uses the following syntax:

Rate CUMIPMT (, nper pv, start, period, end of period, type)

Take, for example, that you paid for the accumulated interest, to 1,000,000 dollars to calculateTen-year equipment loan that charges 9% interest and requires monthly payments of a pension for arranged. Further, suppose you want the cumulative interest payments in the first five years, or sixty months to calculate. To make this calculation, use the following formula:

CUMIPMT = (.09/12, 10 * 12,1000000,1,60,1)

The function returns the value of -360,094.

With the function CUMPRINC

The CUMPRINC function calculates the cumulative principal paid on a loanbetween two dates you specify as changing the interest rate, credit, credit cash value, start and end dates and the type-of-retirement. It uses the following syntax:

CUMPRINC (rate, ZZR, BW, period, end of period start, type)

Take, for example, that the cumulative amount of capital at a $ 1,000,000 ten-year equipment loans that charge the fees paid 9% interest and requires monthly payments of a pension arranged motion. Further, suppose you want to calculatethe cumulative principal payments during the first five years, months, or sixty. To make this calculation, use the following formula:

CUMPRINC = (.09/12, 10 * 12,1000000,1,60,1)

The function returns the value of -394,303.

User Defined Functions in SQL Server stops coders write redundant code. There are two types of UDFs:
❑ Those that return a scalar value
❑ Those that return a table

//Create Table
create table t_EmployeeInformation
(
employee_ID int identity(1,1) NOT NULL,
employee_Name varchar(50),
employee_EmailID varchar(20)
)

Following code snippet shows a function that returns a scalar value.

//Create Function
create function f_GetEmployeeId(@employee_EmailID varchar(50))
returns int
as
return
(
select employee_ID from t_EmployeeInformation
where employee_EmailID = @employee_EmailID
)


//Use Function
select dbo.f_GetEmployeeId('khan.rahim@gmail.com')


This creates a function that returns a table.

//Create Function
create function f_GetEmployee(@employee_EmailID varchar(50))
returns table
as
return
(
select employee_ID as "ID", employee_Name as "Name"
from t_EmployeeInformation
where employee_EmailID = @employee_EmailID
)

//Use Function
select * from dbo.f_GetEmployee('khan.rahim@gmail.com')


Thanks
A Rahim Khan

In earlier essays, the reader was introduced to the Holy Spirit, learned of His personality, and deity.

A sentence is forming: a definition.

The Holy Spirit is a person.

The Holy Spirit is a person, the third person of the Holy Trinity.

The Holy Spirit is a person, the third person of the Holy Trinity, and is divine.

The Holy Spirit is a divine person within the Holy Trinity who has various ministries.

This is where we pick up: the various ministries of the Holy Spirit.

In business meetings, the first order of business is usually roundtable introductions. These are brief; you must give your name, title, and function in two minutes or less, with the emphasis on less. What sets you apart? What generally identifies you in a business meeting? Your function, what role you play in the organization is what sets you apart. People seek out “go-to” contacts within an organization. If they need what you provide, your name, telephone, and e-mail address is going in their contacts list for future reference.

The ministries of the Holy Spirit provide the same. His functions within the Godhead as well as the body of Christ tell us much about Him; they define Him just as our positions define us. It lets us know that for all things, He is the “go-to” in matters of faith. He seeks us out; we can pursue Him too. He is always there and listening; He is the God who is there. He wants us to “go-to” Him. He has been waiting since before time began to have a moment with you, to abide with you, and offer you everlasting comfort. All you have to do is open that line of communication, let Him come into your heart and life, and He will fill you with the peace that passes all understanding.

So, let’s learn even more about the ministries of the lesser known part of the Godhead.

A Creator, not a Creation

Even with God, humans ask for a starting point. He does not have a beginning per se but He does have a point of entry into the human experiment. Most believe this portal opened in Acts 2 but this is not the case. The Scriptures tell us He was present from the foundations of the World. “Now the earth was ^[a] formless and empty, darkness was over the surface of the deep, and the Spirit of God was hovering over the waters (Gen 1:2 NIV).” Later in the chapter, we read the Godhead’s discourse concerning the forming of man “….let us make man in our own image” thereby confirming the presence of each since the dawn of time as humans know it.

God created all things according to the psalmist David (Psa. 19:1) even though John the Beloved gives credit to God the Son for it (John 1:3,4). If we look to other Scripture passages though we learn the Holy Spirit performed the initial act of creation. So, who takes the credit? All of them do; all of them were present. H.L. Wilmington uses the illustration of God the Father being an executive with a Son, who is an architect with a contractor who is the Holy Spirit.

“Thou sendest forth thy spirit, they are created; and thou renewest the face of the earth (Psalm 104:30 KJV).”

“By His spirit He hath garnished the heavens; His hand hath formed the crooked serpent (Job 26:13 KJV).”

“The spirit of God hath made me, and the breath of the Almighty hath given me life (Job 33:4 KJV).”

“Then he said to me, “Prophesy to the breath; prophesy, son of man, and say to it, ‘This is what the Sovereign LORD says: Come from the four winds, O breath, and breathe into these slain, that they may live.’ (Ezekiel 37:9 NIV).“

Dr. James Kennedy writes in his work, Why I Believe, “I believe in the Holy Spirit not only because of who the Bible says He is but because of what the Bible says He does. The Scriptures give us an amazing report of His activities. Certainly, the list is far too long to include here, but among His works are: He created the world, the world being created out of the Father through the Son and by the Holy Spirit. The Holy Spirit inspired the writing of the Scriptures so that the Bible is not like any other book; but God the Holy Spirit is the author thereof working through the instrumentality of men. The Holy Spirit caused Christ to be conceived in the womb of Mary, of whom it is said, “The Holy Ghost shall come upon thee.” It was the Holy Spirit who baptized Jesus [descended as a dove] who led him and empowered Him. The Holy Spirit is also described as having raised Jesus from the dead (146).” The Holy Spirit, being poured out upon the people, was responsible for the added 3,000 to the family of God on that day called Pentecost. And it is the Holy Spirit who indwells the lost soul and redeems it for all eternity. It is through Him that we may cry “Abba, Father!” Is there anything too great for Him? Is there anything He cannot do? No, He can do anything He wills. He is God.

Plenary Verbal Inspiration, God-Breathed Revelation

The blessed Holy Spirit is the author of the Scriptures. As the Spirit moved, so did the hearts of men stir to bring about the Holy Writ known today as God’s Word. His authorship is verified by the following men of God.

1) David: “The spirit of the Lord spake by me, and his word was in my tongue (2 Samuel 23:2 KJV).”

2) Isaiah: “As for me, this is my covenant with them, saith the Lord; My Spirit that is upon thee, and my words whichI have put in thy mouth, shall not depart out of thy mouth, nor out of the mouth of thy seed, nor out of the mouth of they seed’s seed, saith the Lord, from henceforth and for ever (Isaiah 59:21 KJV).”

3) Jeremiah: “Then the Lord put forth his hand, and touched my mouth, And the Lord said unto me, Behold, I have put my words in thy mouth (Jeremiah 1:9 KJV).”

4) Jesus: “For verily I say unto you, till heaven and earth pass, on jot or one tittle shall in no wise pass from the laws, till all be fulfilled (Matthew 5:18 KJV).”

5) Peter: “For the prophecy came not in old time by the will of man; but holy men of God spake as they were moved by the Holy Ghost (2 Peter 1:21 KJV).”

6) Paul: “And that from a child thou has known the holy scriptures, which are able to make thee wise unto salvation through faith which is in Christ Jesus. All scripture is given by inspiration of God, and is profitable for doctrine, for reproof, for correction, for instruction in righteousness: that the man of God may be perfect, thoroughly furnished unto all good works (2 Timothy 3:15-17 KJV).”

7) John: “In the beginning was the Word…”

¹In the beginning was the Word, and the Word was with God, and the Word was God.

²The same was in the beginning with God.

³All things were made by him; and without him was not any thing made that was made.

⁴In him was life; and the life was the light of men.

⁵And the light shineth in darkness; and the darkness comprehended it not.

⁶There was a man sent from God, whose name was John.

⁷The same came for a witness, to bear witness of the Light, that all men through him might believe.

⁸He was not that Light, but was sent to bear witness of that Light.

⁹That was the true Light, which lighteth every man that cometh into the world.

¹⁰He was in the world, and the world was made by him, and the world knew him not.

¹¹He came unto his own, and his own received him not.

¹²But as many as received him, to them gave he power to become the sons of God, even to them that believe on his name:

¹³Which were born, not of blood, nor of the will of the flesh, nor of the will of man, but of God.

¹⁴And the Word was made flesh, and dwelt among us, (and we beheld his glory, the glory as of the only begotten of the Father,) full of grace and truth.

¹⁵John bare witness of him, and cried, saying, This was he of whom I spake, He that cometh after me is preferred before me: for he was before me.

¹⁶And of his fulness have all we received, and grace for grace.

¹⁷For the law was given by Moses, but grace and truth came by Jesus Christ.

¹⁸No man hath seen God at any time, the only begotten Son, which is in the bosom of the Father, he hath declared him.

¹⁹And this is the record of John, when the Jews sent priests and Levites from Jerusalem to ask him, Who art thou?

²⁰And he confessed, and denied not; but confessed, I am not the Christ.

²¹And they asked him, What then? Art thou Elias? And he saith, I am not. Art thou that prophet? And he answered, No.

²²Then said they unto him, Who art thou? that we may give an answer to them that sent us. What sayest thou of thyself?

²³He said, I am the voice of one crying in the wilderness, Make straight the way of the Lord, as said the prophet Esaias.

²⁴And they which were sent were of the Pharisees.

²⁵And they asked him, and said unto him, Why baptizest thou then, if thou be not that Christ, nor Elias, neither that prophet?

²⁶John answered them, saying, I baptize with water: but there standeth one among you, whom ye know not;

²⁷He it is, who coming after me is preferred before me, whose shoe’s latchet I am not worthy to unloose.

²⁸These things were done in Bethabara beyond Jordan, where John was baptizing.

²⁹The next day John seeth Jesus coming unto him, and saith, Behold the Lamb of God, which taketh away the sin of the world.

³⁰This is he of whom I said, After me cometh a man which is preferred before me: for he was before me.

³¹And I knew him not: but that he should be made manifest to Israel, therefore am I come baptizing with water.

³²And John bare record, saying, I saw the Spirit descending from heaven like a dove, and it abode upon him.

³³And I knew him not: but he that sent me to baptize with water, the same said unto me, Upon whom thou shalt see the Spirit descending, and remaining on him, the same is he which baptizeth with the Holy Ghost.

³⁴And I saw, and bare record that this is the Son of God.

³⁵Again the next day after John stood, and two of his disciples;

³⁶And looking upon Jesus as he walked, he saith, Behold the Lamb of God!

³⁷And the two disciples heard him speak, and they followed Jesus.

³⁸Then Jesus turned, and saw them following, and saith unto them, What seek ye? They said unto him, Rabbi, (which is to say, being interpreted, Master,) where dwellest thou?

³⁹He saith unto them, Come and see. They came and saw where he dwelt, and abode with him that day: for it was about the tenth hour.

⁴⁰One of the two which heard John speak, and followed him, was Andrew, Simon Peter’sbrother.

⁴¹He first findeth his own brother Simon, and saith unto him, We have found the Messias, which is, being interpreted, the Christ.

⁴²And he brought him to Jesus. And when Jesus beheld him, he said, Thou art Simon the son of Jona: thou shalt be called Cephas, which is by interpretation, A stone.

⁴³The day following Jesus would go forth into Galilee, and findeth Philip, and saith unto him, Follow me.

⁴⁴Now Philip was of Bethsaida, the city of Andrew and Peter.

⁴⁵Philip findeth Nathanael, and saith unto him, We have found him, of whom Moses in the law, and the prophets, did write, Jesus of Nazareth, the son of Joseph.

⁴⁶And Nathanael said unto him, Can there any good thing come out of Nazareth? Philip saith unto him, Come and see.

⁴⁷Jesus saw Nathanael coming to him, and saith of him, Behold an Israelite indeed, in whom is no guile!

⁴⁸Nathanael saith unto him, Whence knowest thou me? Jesus answered and said unto him, Before that Philip called thee, when thou wast under the fig tree, I saw thee.

⁴⁹Nathanael answered and saith unto him, Rabbi, thou art the Son of God; thou art the King of Israel.

⁵⁰Jesus answered and said unto him, Because I said unto thee, I saw thee under the fig tree, believest thou? thou shalt see greater things than these.

⁵¹And he saith unto him, Verily, verily, I say unto you, Hereafter ye shall see heaven open, and the angels of God ascending and descending upon the Son of man (John 1:1-51 KJV).”

To Be Continued:

Next Up: The Ministry of the Holy Spirit, Part Two

Saturday was my final shift in Tompkins, we stayed up for drinks till 4.30am. Woohoo! It was good. Tash was so lovely, she brought us chips, chocolates, chicken salads & turkey. She’s like the best manager I ever had. I want to thank everyone in Tompkins Park, you guys made my stay in Perth very memorable. HUGS!

Faces of Tompkins Park

Working in Fremantle Town Hall on Fri. FUN!

Last week was insanely busy! Sun = Brisbane Bar ; Mon = city ; Tues = Beach ; Wed = Shopping in city & dinner in Matsuri with Hwee Ping ; Thurs = work from 7.30am to 2pm followed by shopping till 8pm ; Fri = 14 hours of work straight; Sat = last day in Tompkins.

Events for this week: Sun = Brisbane Bar (again) with Rhiannon, Fabi, John & Jesper, followed by supper in chinatown till 2.30am ; Mon = uni, Garden City & packing ; Tues = BBQ at Fabi’s ; Wed = packing & shopping ; Thurs = Flight SQ226 back to S’pore ; Fri = shopping for suit, Sweden Embassy, pre-placement briefing in city; Sat = Parrtyyy!

Nazroo& his elephant, Rajan, in Havelock, Andaman Islands

The sweetest pic! A photo of the photographer’s grandparents

I love photos of trees … i pick this as one of my fav

The edge of an iceberg floating just off the coast of Antarctica

Innocently adorable

As I mentioned earlier in my previous post, Seagulls are scary …

P.S. I’ve finally created my new header. Woohoo! Now reluctantly, back to packing…

the return, after a three year hiatus, Adam Parkinson brings back LSD to Newcastle – expect fizzy noise, heavy bass, cracks, acidic forays & bastard pop from OX & BULL. Should be a blast..

here’s the promotional mix – it’s great, a potent blend including War Against Sleep, Gold Panda, Nite Jewell and more at sea on an ocean of dissonance. Attend.
Love’s Secret Domain Mix by adam parkinson

Basic Graphing

You can graph in by typing equations of functions in the Input box.

Type the following equations of functions in the Input box and press the ENTER key after each equation.

1. y = 2x + 3
2. f(x) = -3x + 5
3. 2x – 3y + 6 = 0
4. g(x) = sin(x)
5. y = x^3 – 1

Notes:

• You can type linear equations in the following forms:  y = ax + b, f(x) = a(x) + b or ax + by + c = 0.
• The * is used in multiplication and ^ is used in exponentiation. For example you want to graph, y = 2(x – 3)², then you should enter y = 2*(x-3)^2.

Properties of Graph

You can change the  labels, colors, thickness and other properties of graphs (and other objects) in GeoGebra. In this tutorial we are going to change the color, label and thickness of the graph g(x) = sin(x).

To change the properties of the graph g(x) = sin(x), do the following:

1.)    Right click the graph of the sine function then click Object Properties from the context menu.

Figure 2 - The context menu that appears when you right-click a graph

2.)    In the Basic tab, be sure that the Show label check box is checked.

3.) Choose Name and Value from the Show label drop-down list box.

Figure 3 - The Basic tab of the Properties dialog box

4.)    To change the color, click the Color tab, then choose your color from the Color palette.

5.)    To change the thickness of the graph, click the Style tab, move the slider bar to 5.

Figure 4 - The Style tab of the Properties dialog box.

6.)    Click the Close button

Exercise: Change the properties of the other graphs. Explore the options in the Properties dialog box and see their effects to the graphs.

You may also want to view another tutorial on graphs and sliders.

Oracle Packages, Procedures, Functions

http://www.oraclepassport.com/Oracle%20Packages.html

Please send resumes to rrabines@topsource.com

Location: Boca Raton, FL

Title: Reports Developer / SSRS

Salary: $60,000 – $65,000/year + Benefits

The ideal Reports Developer will need to be effective developing in MS SQL.

Responsibilities:

-     Monitors integration logs and effectively debugs and resolves issues

-     Manages regular data integration updates from schools which involves managing school data loads; school and campus metadata, school lead forms, lead caps, lead delivery, and all respective web site mappings to schools and their respective program offerings

-     Launches school integrations with new customers in a timely manner.

-     Manages day-to-day interaction and expectations with Sales

-     Works effectively with peers in IT

-     Ensures deliverables for projects are well documented, approved, and prioritized by management

-     Ensures changes to project schedule and/or scope are reviewed and approved

-     Ensures all initiatives follow our SDLC methodology

-     Leads the testing efforts for integration

-     Effectively communicates relevant project information

-     Resolves and/or escalates issues in a timely fashion

Requirements:

-     3+ years experience developing in MS SQL Server (stored procedures, functions, views)

-     3+ years experience developing MS SQL reports using SSRS

-     3+ years experience working with stakeholders

-     3+ years using advanced features in Excel working with raw data and reporting

-     Experience working in a Microsoft .NET environment with specific aptitude using xml and web services.

-     Experience working within an enterprise IT environment

-     Participate in on-call production support, providing off-hour support as appropriate

-     Represents the organization and self professionally

-     Effective time management and organization skills

-     Ability to work on multiple projects

-     Excelling verbal and written communication skills

-     Ability to work within team environment

-     Ability to work independently

-     Ability to be a self starter to promote new initiatives

This year we are trying the age old method of bribery to get people to book functions. In addition to our very reasonably priced menus and our fantastic sustainable fair.
we are offering a gift boxed bottle of veuve to the person who books any function that chooses beverage package 2 from our function packaeg $39 per person ( chandon NV, Mr Riggs And Cape Mentelle Sem Sauv Blanc). Not ionly are the wines a good deal but you also get to walk home with a bottle of french. Or you could simply add it to the parties festivities.  Download function packages Here

P.S we also have a Private dining room which takes up to 24 people for those special functions or private functions. the private dining room has its own stereo, waiter, and bar. perfect for a special birthday, or corporate event.

Today, we investigated homomorphisms further. Recall that a homomorphism between two groups and is a function such that
for all .

This basically says that the function “understands the operations of the group” and maps elements in a way that is compatible with the operations of the respective groups. We saw many examples of homomorphisms, some of which we already knew. For instance:

• 
• by and
• by

are all homomorphisms between their respective groups. There are many more examples as well, and we will continue to investigate different homomorphisms.

Finally, we also noted that if are both groups, then there is always a homomorphism between them given by with where is the identity element in .

We noted that homomorphisms are not quite as strong as isomorphisms, but we will show how much information is actually carried through a homomorphism (as opposed to an isomorphism where all the information is carried through).

Cuando estamos trabajando en un documento de Word 2003 ó 2007, hemos ingresado texto hasta por ejemplo la mitad de la página y necesitamos irnos a una nueva página.

En la mayoría de los casos, presionamos Enter muchas veces hasta llegar a la siguiente página y continuar escribiendo.

Microsoft Word, nos permite crear un salto de página para evitarnos presionar varias veces la tecla Enter.

Para crear un salto de página, presione Ctrl+Enter, y continue escribiendo en la nueva página

If I’m not dating anyone, I would always rather go to an event or function on my own, than find a suitable rent-a-friend to take as my date. Not just because it leaves me free to flirt with any single guys there, but because I find it stressful to be there with someone who is there for the sake of being my ‘plus one’ (note – I’m quite happy to go with a boyfriend).

A few years ago my old junior school was celebrating its centenary and a group of us who’ve been friends for over 25 years decided to take a table at the gala dinner. All the others are married and I thought it might be weird to go on my own, so I asked my friend S if he’d come along as my date. S and I are 100% platonic – I love him to bits as a friend, but we’d last all of 30 seconds as a couple, not to mention that neither of us has had the slightest romantic inclination to the other anyway in the 16 years we’ve known each other.

We arranged to meet outside the function venue and I was relieved to see he had made an effort to dress nicely (although to his credit, he usually does  – and no, he is not gay!). But things went downhill from there. He spent the evening either chatting up a single girl who had joined our party at the last minute (he ended up dating her for a couple of weeks) or ignoring everyone, me included, and having an intense text message exchange with one of his friends-with-benefits. It was so bad that when the evening ended, one of my other friends said, ‘Should I text message S to say goodbye?’

I know S well enough to give him a piece of my mind and not have it ruin our friendship (I think it’s like water off a duck’s back to him actually!). I was furious – I’d asked him to be my date, had paid for his dinner (which was not cheap) and he’d made no effort to ‘accompany’ me or make an effort to be friendly to and interested in the rest of our party (single girl excepted)… embarassing me instead. I would have far preferred to be there on my own instead of having to worry about my date’s behaviour!

Perhaps it’s a sign of the economic times, but I’ve noticed that it’s rare now to get an invitation to a function like a wedding and have ‘plus one / and partner’ included on the invitation. I’m quite happy about that – the pressure of finding someone to go with and the stress of wondering whether he’ll behave is something I can do without

http://docs.google.com/gview?a=v&pid=gmail&attid=0.1&thid=1250d417d3e990a6&mt=application%2Fvnd.ms-powerpoint&url=http%3A%2F%2Fmail.google.com%2Fmail%2F%3Fui%3D2%26ik%3D0d83c09cfd%26view%3Datt%26th%3D1250d417d3e990a6%26attid%3D0.1%26disp%3Dattd%26zw&sig=AHIEtbR5i17Mh6u10JJUsa-TMS_fJI2DOw

Exponential Functions
You will need Flash Player to see the video.

1.  The following statement represents a multi-row function. True or False?
SELECT MAX(salary)
FROM employees

True (*)
False

2.  The conversion function TO_CHAR is a single row function. True or False?
True (*)
False

3.  Will the following statement return one row?
SELECT MAX(salary), MIN(Salary), AVG(SALARY)
FROM employees;
No, it is illegal. You cannot use more than one multi-row function in a SELECT statement
Yes, it will return the highest salary, the lowest salary and the average salary from all employees (*)
Yes, it will return the highest salary from each employee
Yes, it will return the average salary from the employees table.

4.  The following statement represents a multi-row function. True or False?
SELECT UPPER(last_name)
FROM employees;
True
False (*)

5.  The function COUNT is a single row function. True or False?
True
False (*)

8.1 IA2 Evaluating Functions

8.2 IA2 Function Inverses

8.3 IA2 Function Operations

3304706    ชีวเคมีขั้นสูงของหน้าที่ของเซลล์    Advanced Biochemistry Of Cellular Functions

การศึกษาขั้นสูงในโครงสร้างของเซลล์และหน่วยย่อย สารพันธุกรรม ดีเอนเอ และอาร์เอนเอ การแสดงออกของสารพันธุกรรม พันธุวิศวกรรม กระบวนการต่างๆ ทางชีวเคมีการทำหน้าที่ของเซลล์ แหล่งสะสมเมตาบอลิกและการหมุนเวียน ตัวรับและการสื่อสารของเซลล์ การขนส่งสารผ่านเยื่อหุ้มเซลล์ ชีวสังเคราะห์ของสารที่ออกฤทธิ์ทางเภสัชวิทยาภายในเซลล์

(Advanced study in cell structure and compartments; DNA and RNA as genetic material; gene expression; genetic engineering; biochemistry and of cellular functions; metabolic pools and turnover; receptors and signal transduction; transport across cell membrane; biosynthesis of pharmacological active substances in cells.)

(3304706 จุฬาลงกรณ์มหาวิทยาลัย)

The function is a linear function that satisfies the equation .  Find an expression for .

GeoGebra is capable of graphing a variety of functions as well as computing for areas under a curve.  The screen shot below is an example of several graphs plotted in GeoGebra.

Figure 1 - Graphs created with GeoGebra

In this tutorial, we are going to use GeoGebra to investigate the effects of parameters of functions to its graph. Unlike in our previous activities, this time we are going to use the Algebra window and the coordinate axes. First, we are going to investigate the graph of by typing equations in the input field, then later, we are going to use a slider. If you want to follow this tutorial step-by-step, the you can open the GeoGebra window in your browser. The output of this tutorial can be viewed here.

Update (Nov 24, 2009): I have also created another Slider article entitled Graphs and Sliders Part 2.

Graphing Functions

1. Open GeoGebra. To graph , type y = 2x in the input field. (The input field is the text box with the label Input located at the bottom of your GeoGebra window.) Press the ENTER key on your keyboard.
2. Type the following equations: , and, and press the enter key after each equation.
3. Type more equations of the form where m is any real number.
4. How does the value of affect the appearance of the graph of the function ?

Using Sliders

To avoid typing over and over again for varying values of parameters , we will use the slider control.  A slider is a visual representation of a number. This time, we will also add the parameter b. This means that we will explore the graph of the function of , where  and are real numbers.

	1.) Open the Geogebra window.
	2.) Select the Slider control and click anywhere on the drawing pad do display the Slider dialog box.
	3.) In the Slider dialog box, change the slider’s name to m, change the interval to to as shown below.   Figure 2 - The Slider Dialog Box Leave the other values as is and click the Apply button to finish.
	4.) Adjust the position of your slider if necessary. Move the small black circle on your slider. What do you observe?
	5.) To graph the function ,  type y = m*x in the Input box.
	6.) Now, move the small circle on your slider. What do you observe?
	7.) Now, create a new slider and name it . Set the interval to and leaving the other values as is.
	8.) To change the function to , right click the graph, click Redefine from the context menu, and type y = m*x + b.
	9.) Now, move your  slider. What do you observe?
	10. ) How does the value of affect the appearance of the graph of the function ?
	11.)  Graph the function . Explain the effects of the parameters a and b to the graph of the function.

Notes:

1. The ^ symbol is used for exponentiation in GeoGebra. Hence, we write as a*x^2 + c.
2. Instead of using in writing equations of functions, you can also use for the function .