Tuesday, January 16, 2007
posted by DestiniLyn at 7:01 p.m.
Monday, January 15, 2007.

Sorry everyone, I wasn't able to blog last night because my internet wasn't working. But we had someone come over tonight & fix it so, yay! :)

So far during this unit we've looked at:

• Relations ; "Any set of Ordered Pairs." Example: (0,1) (2,3) (2,7) (-3,9) ...
• Functions ; " (A type of Relation) Each x value can only have one corresponding y value."
• Sequences ; " (A specific type of function) A list of numbers that have a particular pattern."

Today, we looked at Arithmatic Sequences.

Arethmatic Sequences are a list of numbers where the difference between consecutive terms is the same.

Example: 10 , 12 , 14 , 16 , 18 . . .

Since 10 is the first number in the sequence, it is called Term One or T1. 12 is the second number in the sequence, so it is called Term Two or T2.

With this sequence, there is a difference of 2 between each term. All Arithmatic Sequences create a straight line. ie: A Linear Equation. ( y = mx + b )

mx = The difference between consecutive terms

b = T1. ( Term One. )

d = The difference between terms.

tn = The Nth Term.

Here are some more examples that we did together in class...

For the following Arithmatic Sequences, determine the function that represents the list of munbers...

1.) 3 , 6 , 9 , 12 . . .

There is a differnce of 3 between each term, so d = 3

This means that the slope (or mx) is equal to 3/1

f(x) = 3x [ (x) is the term number. ]

f(1) = 3(1)

f(2) = 3(2) . . . (FUNCTION)

2.) 5 , -3 , -11 , -19 . . .

There is a differnce of -8 between each term, so d = -8.

This means that the slope ( or mx ) is equal to -8/1

So, starting at 5... take the difference (-8)

-8 --->5 = 13. (5 - -8 = 13)

f(x) = -8x+13. (IS NOT A DIRECT FUNCTION)

Now, to find the Nth Term...

tn = t1 + (n-1)d

t1 = First Term

n = Unknown Number

d = The Difference

Here are some examples...

1.) 8 , 16 , 24 . . . What is the 11th Term? (t11)

There is a difference of 8, so d = 8

So.. t11 = 8 + (11-1) 8 ... 8 + (10) 8 = 88 t11 = 88

2.) 2.2 , 1.1 , 0 , -1.1 . . . What is the 19th Term? (t19)

There is a difference of 1.1, so d = 1.1

So... t19 = 2.2 + (19-1) 1.1 ... 2.2 + (18) 1.1 = 17.6 t19 = 17.6

Homework was Excercises 58 (1-8) & 59 (1-11)

The next person to blog is Edward. :P

Monday, January 15, 2007
posted by man at 10:51 p.m.
To late for posting.lol!Well this is last mondays lesson.Relation(Domain and Range)

"Relation"

A relation is any subset of a Cartesian product. For instance, a subset of , called a "binary relation from to ," is a collection of ordered pairs with first components from and second components from , and, in particular, a subset of is called a "relation on ." For a binary relation , one often writes to mean that is in .

Eg.

(2,0),(1,5),(3,8),(4,1) ...(any set of ordered pairs are "relation")

The concept of a relation is a generalization of 2-place relations, such as the relation of equality, denoted by the sign "=" in a statement like "5 + 7 = 12," or the relation of order, denoted by the sign "<" in a statement like "5 < 12". the concept of a relation is a generalization of 2-place relations, such as the relation of equality, denoted by the sign "=" in a statement like "5 + 7 = 12," or the relation of order, denoted by the sign "<" in a statement like "5 < 12".

Relations are classified according to the number of sets in the cartesian product, in other words the number of terms in the expression:

Unary relation or property: L(u)

Binary relation: L(u, v) or u L v

Ternary relation: L(u, v, w)

Quaternary relation: L(u, v, w, x)

Domain and Range

Domain:

For a function f defined by an expression with variable x, the implied domain of f is the set of all real numbers variable x can take such that the expression defining the function is real. The domain can also be given explicitly.

Range:

The range of f is the set of all values that the function takes when x takes values in the domain.
The y-values.

This list of points, being a relationship between certain x's and certain y's, is a relation. The domain is all the x-values, and the range is all the y-values. You list the values without duplication:
{(2, –3), (4, 6), (3, –1), (6, 6), (2, 3)} This are the set of numbers.

domain: {2, 3, 4, 6}

range: {–3, –1, 3, 6}

You can see how we put the numbers in domain and range. All the x were put to domain and all y were put in range..

Sunday, January 14, 2007
posted by Jhonaleen at 6:54 p.m.
On Friday's math class, we went through three things, graphing data, direct variation and Go For Gold.

Graphing Data
Ms. Armstrong took the guesswork out of deciding which information from a table of values is the dependent variable, and which is the independent variable. Even though we know that the dependent variable "relies" on the independent variable (eg. time and speed ; in this case, time would be the independent variable since the speed depends on the time that has elapsed), we learned that the first column of a table of values is always the independent variable.

Direct Variation
Definition:
A relationship between two variables in which one is a constant multiple of the other. In particular, when one variable changes the other changes in proportion to the first.

When two variable quantities have the the same ratio, they have what is called direct variation.
(This is the diagram/example we were given.)

So, in the diagram, ' p= 8h ', making it a linear function, since it's the same as ' y = mx+b ' but in
' p = 8h ' b = 0 This means that whenever b = 0, you have direct variation.
We were given other examples, too.

p = 6t + 2 <-- NOT direct variation y = 3x <-- direct variation y = -2x + 0 <-- direct variation To connect the previous lesson with this one, it is possible to write, what is called, a direct variation function. How? y = kx *In this equation, 'k' stands for 'constant' We were asked to write an equation for the following statement: The cost of selling items at \$0.25 varies directly with the number of items sold.
c -> cost n -> number of items sold
c varies directly with n (this means that the cost is always determined by how many items are sold)
So, the equation would be: c = 0.25n

Exercise 46 #1-9
Exercise 57 #1-14, 17

* * * For extra help, visit this link: http://www.freemathhelp.com/direct-variation.html * * *

Go For Gold
The last part of the class was taken up by receiving our Go For Gold booklets. It consists of 25 pages, and has multiple choice, short answer and long answer questions. Basically, we were told:
- it's worth 10% of our mark, and it's either 0% or 100%.
- even though you can ask for help, Ms. Armstrong will check your booklet ONCE, and only once. - you can ask others for help, compare and work together in a study group.
- you must show your work for EVERY question.
- last, but definitely not least, DUE DATE: Monday, January 22nd

The next blogger is Christine.

posted by dondelacruz_ at 10:18 a.m.
Today we did more on functions

What Is a Function you ask?

A function is a special type of relation where each x-value in the domain corresponds to ONLY 1 y-value in the range.

example: Graph f(x)= x-1 means the same as y=x-1

D:{xER}
R:{xER}

y-intercept --> f(0)=x-1
=0-1
=-1

the zeros of the function are the x-intercept(let y=0)
f(x)=x-1
0=x-1
1=x

to find zero let F(x)= 0

Graph, find D and R and the zeros for f(x)=3/2x-3

D:{xER}
R:{xER}

zeros: f(x)=3/2x-3
0=3/2x-3
2(3)=(3/2)2x
6=3x
2=x

f(x)=1/2x-3
0=1/2x-3
2(3)=(1/2)2x
6=x

linear functions f(x)=mx+b
constant functions f(x)=b <-- has no x value

will always be a straight line.
f(x)=-4

HOMEWORK: ex. 54 # 1-9, 12
55 # 1-7

Thursday, January 11, 2007
posted by Paulo at 7:27 p.m.
Ok...this is what happened on Wednesday. Functino and Function Notation.

What is a Function?

A Function is a special type of relation where each x-value in the domain corisponds to only 1 y-value in the range.

EG.

2 ==>8
0 ==>4
==>6
6 ==>3

Ordered Pairs: (2,8),(0,4),(0,6),(6,3)

As you can see in the ordered pairs the x-value of 0 has two different y-values. THIS IS AN EXAMPLE OF A RELATION, NOT A FUCTION.

That was an example of using the ordered pairs. What if we were given a graph? Why use the Vertical Line Test!

What is the vertical line test? Well its the test used on graphs to see if it is a function or a relation. If the line passes through two points or more on the graph then it is a relation. If it passes through only one point then it is a Function.

Here are a few Examples from class.

You know that this is a function right? The vertical line test shows it is. Anywhere on the graph if you drew a vertical line there it would only go through one point.

On to the next graph.

This is also a function. No line going through two points

This is a relation. Not a function. As you can see there is a vertical line in the graph. If you put a vertical line through that it over laps. Which means that its going through more then one point. If you drew it anywhere else it would not hit more then two points, but because of that vertical line the graph made it is considered a relation.

This one is in the same boat as the last one. It is a relation becaues there are three points in a line. If you drew a vertical line there it would hit all three. Therefore it is a relation.

Okay I know that this is gettign repetitive right about now, but now moving on to the other topic that was covered on wednesday.

Function Notation

Functions are usually represented with the letters "F" or "G"

Eg. f (x) = x + 2

This reads "The value of the function at this value of x is x +2"

Lets try doing a question from class , the one above. Well i think there is suppose to be a stament about what you switch f (x) with...but it seems i dont have it, I am very sorry for this. I do have the work though

f (x) = x + 2
f (3) = 3 + 2 ====> What ever you switch the x with on the right side you switch all the x's on the left side with the same thing and just evaluate left side. I am really sorry for how i said that and i know it should be something else mathematical, but i really dont know any other way to day it. ANYWAYS...continuing on.
f (3) = 5

Okay that was the easy one. Now we go into Compound Functions.

Let f (x) = x2 / x + 1 and g (x) = 4 / x2

1.f (g(2))

This may seem confusing at first but it really isnt that hard. You work your way inside out. You start with the g (2) function and find that. the you use that in the f function. Heres the work.

Oh we are replacing the x value with 2

g (x) = 4 / x2
g (2) = 4 / 22
g (2) = 4 / 4
g (2) = 1

After you get that done just your answer you got from the g function and use it in the in function.

f (g(2))

It will be this.

f (1)

To finish the problem your going finish with the f function

f (x) = x2 / x + 1
f (1) = 12 / 1 + 1
f (1) = 1 / 2
f (g(2)) = 1 / 2

And thats Wednesday's class. I picked don already to scribe and it should be up today too so i dont need to pick one again.

posted by Ms. Armstrong at 12:08 p.m.
Hey Gummy Bears,
I thought you might enjoy this Jeopardy Game that quizzes you on relations, functions, and direct variation. Make sure you use function notation when typing in your answer or it will mark you incorrect. For example...If it asks what is the function, you can't type in 2x+3 . You must type f(x)=2x+3.

Wednesday, January 10, 2007
posted by michele h at 12:12 a.m.
It's quite facinating actually, there are a lot of numbers that come after "trillion". I searched it up on google and luckily I found a site where it gives a whole bunch of numbers that come after trillion. Here see for yourself:

thousand 1,000
1. million
1,000,000
2. billion
1,000,000,000
3. trillion
1,000,000,000,000
1,000,000,000,000,000
5. quintillion
1,000,000,000,000,000,000
6. sextillion
1,000,000,000,000,000,000,000
7. septillion
1,000,000,000,000,000,000,000,000
8. octillion
1,000,000,000,000,000,000,000,000,000
9. nonillion
1,000,000,000,000,000,000,000,000,000,000
10. decillion
1,000,000,000,000,000,000,000,000,000,000,000
11. undecillion
1,000,000,000,000,000,000,000,000,000,000,000,000
12. duodecillion
1,000,000,000,000,000,000,000,000,000,000,000,000,000
13. tredecillion
write 1,000 followed by 13 groups of three zeros
14. quattuordecillion
1,000 followed by 14 groups of three zeros
15. quindecillion
1,000 followed by 15 groups of three zeros
16. sexdecillion
1,000 followed by 16 groups of three zeros
17. septendecillion
1,000 followed by 17 groups of three zeros
18. octodecillion
1,000 followed by 18 groups of three zeros
19. novemdecillion
1,000 followed by 19 groups of three zeros
20. vigintillion
1,000 followed by 20 groups of three zeros
21. unvigintillion
1,000 followed by 21 groups of three zeros
22. duovigintillion
1,000 followed by 22 groups of three zeros
23. trevigintillion
1,000 followed by 23 groups of three zeros
24. quattuorvigintillion
1,000 followed by 24 groups of three zeros
25. quinvigintillion
1,000 followed by 25 groups of three zeros
26. sexvigintillion
1,000 followed by 26 groups of three zeros.
27. septenvigintillion
1,000 followed by 27 groups of three zeros
28. octovigintillion
1,000 followed by 28 groups of three zeros
29. novemvigintillion
1,000 followed by 29 groups of three zeros
30. trigintillion
1,000 followed by 30 groups of three zeros
31. untrigintillion
1,000 followed by 31 groups of three zeros
32. duotrigintillion
1,000 followed by 32 groups of three zeros
33. tretrigintillion
1,000 followed by 33 groups of three zeros
34. quattuortrigintillion
1,000 followed by 34 groups of three zeros
35. quintrigintillion
1,000 followed by 35 groups of three zeros
36. sextrigintillion
1,000 followed by 36 groups of three zeros
37. septentrigintillion
1,000 followed by 37 groups of three zeros
38. octotrigintillion
1,000 followed by 38 groups of three zeros
39. novemtrigintillion
1,000 followed by 39 groups of three zeros
1,000 followed by 40 groups of three zeros
1,000 followed by 41 groups of three zeros
1,000 followed by 42 groups of three zeros
1,000 followed by 43 groups of three zeros
1,000 followed by 44 groups of three zeros
1,000 followed by 45 groups of three zeros.
1,000 followed by 46 groups of three zeros
1,000 followed by 47 groups of three zeros
1,000 followed by 48 groups of three zeros
1,000 followed by 49 groups of three zeros
50. quinquagintillion
1,000 followed by 50 groups of three zeros
51. unquinquagintillion
1,000 followed by 51 groups of three zeros
52. duoquinquagintillion
1,000 followed by 52 groups of three zeros
53. trequinquagintillion
1,000 followed by 53 groups of three zeros
54. quattuorquinquagintillion
1,000 followed by 54 groups of three zeros
55. quinquinquagintillion
1,000 followed by 55 groups of three zeros
56. sexquinquagintillion
1,000 followed by 56 groups of three zeros
57. septenquinquagintillion
1,000 followed by 57 groups of three zeros
58. octoquinquagintillion
1,000 followed by 58 groups of three zeros
59. novemquinquagintillion
1,000 followed by 59 groups of three zeros
60. sexagintillion
1,000 followed by 60 groups of three zeros
61. unsexagintillion
1,000 followed by 61 groups of three zeros
62. duosexagintillion
1,000 followed by 62 groups of three zeros
63. tresexagintillion
1,000 followed by 63 groups of three zeros
64. quattuorsexagintillion
1,000 followed by 64 groups of three zeros
65. quinsexagintillion
1,000 followed by 65 groups of three zeros
66. sexsexagintillion
1,000 followed by 66 groups of three zeros
67. septensexagintillion
1,000 followed by 67 groups of three zeros
68. octosexagintillion
1,000 followed by 68 groups of three zeros
69. novemsexagintillion
1,000 followed by 69 groups of three zeros
70. septuagintillion
1,000 followed by 70 groups of three zeros
71. unseptuagintillion
1,000 followed by 71 groups of three zeros
72. duoseptuagintillion
1,000 followed by 72 groups of three zeros
73. treseptuagintillion
1,000 followed by 73 groups of three zeros
74. quattuorseptuagintillion
1,000 followed by 74 groups of three zeros
75. quinseptuagintillion
1,000 followed by 75 groups of three zeros
76. sexseptuagintillion
1,000 followed by 76 groups of three zeros
77. septenseptuagintillion
1,000 followed by 77 groups of three zeros
78. octoseptuagintillion
1,000 followed by 78 groups of three zeros
79. novemseptuagintillion
1,000 followed by 79 groups of three zeros
80. octogintillion
1,000 followed by 80 groups of three zeros
81. unoctogintillion
1,000 followed by 81 groups of three zeros
82. duooctogintillion
1,000 followed by 82 groups of three zeros
83. treoctogintillion
1,000 followed by 83 groups of three zeros
84. quattuoroctogintillion
1,000 followed by 84 groups of three zeros
85. quinoctogintillion
1,000 followed by 85 groups of three zeros
86. sexoctogintillion
1,000 followed by 86 groups of three zeros
87. septoctogintillion
1,000 followed by 87 groups of three zeros
88. octooctogintillion
1,000 followed by 88 groups of three zeros
89. novemoctogintillion
1,000 followed by 89 groups of three zeros
90. nonagintillion
1,000 followed by 90 groups of three zeros
91. unnonagintillion
1,000 followed by 91 groups of three zeros
92. duononagintillion
1,000 followed by 92 groups of three zeros
93. trenonagintillion
1,000 followed by 93 groups of three zeros
94. quattuornonagintillion
1,000 followed by 94 groups of three zeros
95. quinnonagintillion
1,000 followed by 95 groups of three zeros
96. sexnonagintillion
1,000 followed by 96 groups of three zeros
97. septennonagintillion
1,000 followed by 97 groups of three zeros
98. octononagintillion
1,000 followed by 98 groups of three zeros
99. novemnonagintillion
1,000 followed by 99 groups of three zeros
100. centillion
1,000 followed by 100 groups of three zeros

One GOOGOL is a ONE followed by 100 zeroes.
One GOOGOLPLEX is a ONE followed by one googol zeroes
(you can't write a googolplex, even in a million years)

this information was taken off of this site: http://utterlyboring.com/archives/2003/09/10/what_comes_after_trillion.php
I'm not quite sure if this is very accurate but it's pretty neat huh?

So the question now is, what comes after googoplex? Infinity?
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