Monday, 7 January 2013

01 POLYNOMIAL - FUNCTIONS

Dear 302s,

Welcome to the very first Mathematics Lesson of the year 2013.

We will be looking at FUNCTIONS & RELATIONS to start off the year...

So what exactly is a Function?

Click on this to find out more about Functions....

A Function has input and output. A good analogy of this would be a vending machine.
1) Explain further why this analogy is used to depict a function?

2) Can you think of other analogy?

3) What are the assumptions made?

Input your answers to the aboved 3 questions under the comment section.

1. 1) This has a required input (coin/money) which will result in a output (chosen kind of food)

2) Electronic notes-coin changer

3) Assumptions is that there will be something required (a) for a set number or another equivalent of a different item (b) and such that only a = b

2. 1) Explain further why this analogy is used to depict a function?

A certain amount of something will go into the equation and will come out with a different amount.

2) Can you think of another analogy?

A fuel tank giving a certain amount of mileage

3) What are the assumptions made?

The equation controlling the quantities of both sides is fixed.

3. 1) This analogy is sued to describe a function for it has many parts to a working system for the food to be delivered to the consumer after putting the correct amount of money into the machine.

2) A clock

3) Assumptions made are that there parts to create an active structure.

Nicole Heng

4. 1) It is a good analogy as when money is put in, u get what you have ordered as the output. Money is the input, food is the output.
2)When someone punches you (input) you get a punch back (output)

3) Any action would have be responded with a reaction

5. 1) There is a input and an output from this vending machine. The input is money while the output is whatever item u chose to buy.

2)Programs.

3) Whatever that inputs will always have a output.

6. This comment has been removed by the author.

7. 1) Explain further why this analogy is used to depict a function?
The analogy is used because Vending Machine depicts the 3 main parts of a function:
The input (The user puts his money into the respective slots)
The relationship (The user interacts with the machine and selects his object in exchange for money)
The output (The selected object gets taken by the user)

2) Can you think of other analogy?
Another analogy is the Input of a CD(Installer for a software) into the mac.
Input: The CD is placed into the CD slot of the mac
Relationship: The CD is used to install the software
Output: The CD is then ejected

3) What are the assumptions made?
The mac isn't spoilt

8. 1) There are only one kind of input (money \$\$) but many different kinds of output. (chips, biscuits, coffee, soft drinks, bread, etc.)

2) Another analogy would be a factory. Raw materials enter the factory and exit it as products.
Other possibilities: Digestive system. Washing Machine. Rolling a ball through a spill of wet paint.

3) The input is different from the output.

9. 1. A vending is used as an analogy to depict a function is because it is similar to the function in the way that it also has an input and an output. When we use a vending machine we put in money(INPUT) to buy the things that we want. Once we have chosen it, it will dispense the item(OUTPUT) that we have chosen.

2. Humans digestive system. After we eat our food, the undigested food is released as faeces.

3. The person is living and has a healthy digestive system.

10. 1. A vending machine is used to depict a function as it shows how a specific input would give an output, as money has to be put in a vending machine in order for a snack or drink to be dispensed.

2. Studying. (input knowledge, output exams....?)

3. The assumption made is that there will definitely be an output.

11. 1) Explain further why this analogy is used to depict a function?
This analogy is used as vending machine has a unique output for different inputs, for example when you put in a certain amount of money, you ar only able to buy stuff that is of equal or of lesser value.
2) Can you think of other analogy?
Another analogy is an ATM.
3) What are the assumptions made?
The ATM is not spoilt and is able to dispense money.

12. 1) If one puts in a different amount of money into the vending machine, one would get a different snack from the vending machine. The analogy reflects how a specific input would lead to a different output.

2) Water cooler. (The harder and longer you press, the more water you will get.)

3) One assumption is that every input, there would be a different output.

13. 1) The Vending Machine works in the same manner as a function. A vending machine takes in money(input), picks out a snack and gives it to(output) the individual who put in the money.

2) Another analogy would be a washing machine. It takes in dirty clothes, washes it, and gives it out as clean clothes.

3) The way a function works is in three stages, input, the middle stage and the output.

14. 1) This analogy is used to depict a function because an input reflects how much output is received.

2) Another analogy is a lightbulb. (the longer you use it, the shorter the lifespan of it.)

3) Assuming that the lightbulb is working.

15. 1) A vending machine has an input which is the money you place in and the output is whatever objects you choose from the machine.

2) Another analogy would be putting fuel into a car and allowing it to function

3) assuming the fuel is able to allow the car to work

16. 1) When money is put into the vending machine, the item that is selected will be dispensed.

2) Another analogy is a DVD player, when a DVD is put in it will be played.

3) There will be an input and a output.

17. 1) There is an input (the money), and an output (the food).

2) Another analogy is a television set. You press a button (input) and the television changes changes (output)

3) There is an output that relates to the input.

18. 1) Explain further why this analogy is used to depict a function?

When someone slots the coins into the vending machine, an item will be dispensed out. It is similar to how a function works, there is an input(coins in) that results in an output. For each individual time an amount of coins is put in, only one food item will be dispensed just like the definition of function.

2) Can you think of other analogy?

Another analogy is saving money up in a coin bank. The longer the number of days, the more money is saved.

3) What are the assumptions made?
One assumption made is that the same amount of money is inputted each day.

19. 1. This analogy is used to depict a function because a vending machine has an input and output like a function. Also, what comes out of the vending machine (the output) is related to how much money you put into the vending machine (the input)

2. Another analogy would be the more pressure applied on a pen, more ink would come out, making the writing look darker

3. An assumption made would be: Each input has its corresponding output.

20. 1.An vending machine is like a function because the buttons you press are in inputs, while the product is the output.

2.Eating and your weight. The more you eat(input), the heavier you get(output)

3. Food causes weight to increase

21. 1. A unique output is given for a specific imput, just like how different items are given when different amounts of money is put into the machine and what item is given depends on the amount of money.

2. A machine that embosses pennies. The imput is the penny, the function is the process of embossing the penny, and the output being an embossed penny.

3. An assumption made is that for every time a penny is inserted into the embossing machine, an embossed penny would be given back.