The point (2,0) on the graph of the square root 
of two less than a number, (x - 2), has been moved 
to each of the following locations by the method listed.

Graph & write an appropriate equation for each graph. 
a. (3,0), shift to the right. 
b. (1,0), shift to the left, & reflection about a 
horizontal line through the point. 
c. (1,0) shift to the left, & reflection about a 
vertical line through the point. 

2	1	0
1	0	1
6	1	2




10/8/07
home screen
soft key pad
zoom
1:box
curser to move
 to a corner of the desired box

  *  graph a line or half circle and adjust the viewing screen
  *  adjust the lightness/darkness
  *  define/rewiew w/web pages vocabulary 
	including home screen, window, softkey pad, xmin
HW: QB picture w/domains & ranges


pg 164: 1-7 pg 57: 6-15
*simplify, evaluate arithmetic expressions
* compute / state slope
* define linear equation, slope, slope-intercept, point-slope, general, standard
* write equations of lines
*  graph lines
RETURN PAPERS
GO OVER GRAPHING PROBLEMS


===============10/10/07 test
1.  Simplify each expression. Write answer on the blank provided.
A.)   4 ÷ 2  	B.)   2 ÷ 4 	C.)   0 ÷ 2 	D.)   2 ÷ 0 
2.  Simplify.  SHOW WORK. WRITE ONE LINE BELOW THE LAST! Write answer on the blank provided.
A.)  27 + 3^2   	B.)   (27 + 3)^2  
C.)  sqrt(169 - 12^2)	D.)   48 ÷ 2 + 4 • 2 
E)   (6 + 5)^2 - 12 • 10 J.)   3^2 + 2^3 + 5^0 
K.)   3 + 2(2 + 3[2(4) + 2(2)] - 1) 
L.)  (- 3)^2   M.) - 3^2   N.  - ( -3)^2
3.  Graph.
A.)  y = 2x + 3	B.)  y = 4 and  x = -3		C.)  2x + 6y = -6
4.  Answer the question asked.  Show work neatly for possible partial credit.
A.)  What is the slope of a horizontal line?
B.)  State the slope of the line containing (4,2) and (-4,-1).
C.)  Write the equation of the line containing (4,2) and (-4,-1).
D.)  State the slope of the line through (3,4) and (2,4).
E.) State the equation of a line through (3,4) and (3,7).
F.) Write the equation of the line graphed here.
<img src="
" align="left">
5.  Create true statements.  Complete the statement using appropriate vocabulary words.
  Coordinate geometry was created by (a)__ (b)__.   It is a powerful blend of algebra and geometry.  
  On a plane, two (c)__    (d)__ cross, usually at right angles, and create a (e)___ (e)__ which permits one to identify each point on the plane.
  Points are named by (f)___ (g)__, with the (h)_ value listed first and the (i)__ value listed second. 
  Lines, points, circles, parabolas, and other curves which were simply drawn historically were able to be written as equations and statements.  (b)_’s work made this possible.  
==============





================
oct 12
  Below, c(t) is the the number of sales in millions of cassettes sold in year t and d(t) is the number of discs sold in year t where t is the number of years beginning with 1990.			October 12, 2007 RED BLUE, Algebra II				
	c(t) = 442.14 - 35.46t, t is between 0 and 7, inclusive							
	d(t)= 279.67 + 78.66t, t is between 0 and 7, inclusive							
a. 	Describe the sales of cassettes in 1990.						
b.	Describe the sales of discs in 1990.			
c.	Predict an outcome at the end of this time period.		
d.	Which sold better at t(0)?							
e.	How many more?							
f.	Display the graphs on an appropriate window and label the domain and range of the window.							
g. 	At what point in time did the sale of one overtake the sale of the other?							
h.	What was the volume at that time?							
==============
10/20 22/07
Linear System Solver   	at  algebra\asyssol.htm © 2007,A. Azzolino 
Solve A System Mentally 	at math\algebra\amental.htm  © 2007,A. Azzolino 
    Study the chart before reading about mentally solving a system. 
    A system may be solved mentally, only if one can recognize parallel or coincident lines. 
    If one line is a multiple of the other, the lines are coincident and have all points in common. An ordered pair for one point is an ordered pair for the other line and a solution to the system. The x-intercept, (?, 0), or the y-intercept, (0,?) are good points to obtain to solve the system. 
    If lines are parallel, they do not intersect so the system has no solution. Recognizing that lines are parallel even before they are graphed is very time efficient.
    If a line is written y= mx + b, the y-intercept is b and the slope is m.
    If a line is written as Ax + By = C, the slope of the line is equal to -A/B.
    If a line is written as Ax + By = C, the y-intercept is equal to C/B.
    If each line in the system has the same slope but a different y-intercept, the lines are parallel and there is no solution.
    If each line in the system has the same slope and the same y-intercept, the lines are coincident.
  Solve the system. 
1.  x - 2y = -2 and     -3x - 6y = -6
2.  y = -2x + 4 and       y = -2x + 5  
3.  5x + 5y = 10       10x + 10y = 12
4.  y = 4x - 1 and      8y = 8x + 8  
Hw: 	Monday 10/22	pg  128-129: orals, 1-31 odd
	Tuesday 10/23	Use Linear Combination & Determinants to Solve Systems 
	Solve the system by linear combination and determinants.    
	1.  x - 2y = -2 and -3x - 6y = -6  		2.  y = -2x + 4 and y = -2x + 5  
	3.  5x + 5y = 10 and 10x + 10y = 12  	4.  y = 4x - 1 and 8y = 8x + 8  
	5. -2x - 2y = -4 and 3x - 8y = -12  	6. -3x+3y=6 and 6x+9y=12  
	7. 4x + 4y = 10 and x + y = 12  		8. 5x+15y=10 and 3x+9y=6  
	Wednesday 10/24	pg 132-134 odds
	Thursday 10/25	pg 132-134 odds, Study for quizzes on systems, and others
==============
10/23/07   blue=========
Solve a system by linear combination.

2y+x=6
4x -2y=12

2x-y= -3
2x-y= -5


2x-y=-3
8x-4y=-12
==============
10/26/07
1.  Write the equation of a line with slope 4 
and y-intercept 6.
y=4x+6
y=mx+b
2.  Write this in standard form.
-4x+y=6
4x-y=-6
3.  Write a line parallel to this.
y=4x+5
y=4x+2

4.  State the array of coefficients and 
constants.

5. State the slope of Ax + By = C.
================
10/29/07
10/29/2007red ================
10/29 Monday	Cramers Rule & word problems	pg 132-134:  1,3,5,7,9,15,19;		
10/30 Tuesday	Cramers Rule & word problems	pg 132-134:  1,3,5,7,9,15,19;		
10/31 Wednesday	half-planes & simplex graphically	pg 138-9: orals, 1-45 odd		
11/1  Thursday	TEST			
11/2  Friday	word problems	pg 132-134:  2,4,6,8,10,12,18		
11/5  Monday	Matrix computation			
11/6  Tuesday	NO SCHOOL			


Solve by substitution is really, " Plug it in. Plug it in."

If     
Ax +By = C 
Dx +Ey = F 
     then        CE-BF 
           x=  ----------------
 	 AE-BD 
     and  
	   AF-CD 
            y = -----------------
 	   AE-BD 
 Write the array of coefficients and constants.

A B C
D E F

Note the cefficient array:
A B
D E

array
matrix - a storage thing organized in rows & columns
determinant - computation wating to be done.
(de)(ter)-(min)(ant)

State the determinant of coefficients,
compute, use this as the denominator.

  |A B |
  |D E | = AE - DB

To get the numerators, write new 
determinants using the constants instead of the 
coefficients for the variable you are solving.

1	20x + 50y = 390	2	20s + 35c= 2280
	x + y = 15		   	        s+c/2=128
==============
10/29/07	Copy:						
10/29 Monday	Cramers Rule & word problems	pg 132-134:  1,3,5,7,9,15,19;				
10/30 Tuesday	Cramers Rule & word problems	pg 132-134:  2,4,6,8,10,12, 18				
10/31 Wednesday	half-planes & simplex graphically	pg 138-9: orals, 1-45 odd				
11/1  Thursday	TEST					
11/2  Friday	word problems	pg 132-134:  2,4,6,8,10,12,18				
11/5  Monday	Matrix computation					
11/6  Tuesday	NO SCHOOL					

Solve.						
1	20x + 50y = 390	2	20s + 35c= 2280			
	x + y = 15			s+c/2=128			
						
3	v+2b=180		4	l+2s=23			
	v=2b-40			l+4s=41	
						
5	25j+18s=441	6	x+y=30			
	20j+20s=420		20x+15y=510			
						
7	(h+w)(5/3)=300	8	(h+w)(4)=1000			
	(h-w)(2)=300		(h-w)(10/3)=1000			
						
9	1f+6a=100		10	f+25g=300		
	1f+3a=640			f+40g=420	
						
						
11	x+y=8000		12	p=a+3			
	.06x+.15y=930		28p+15a=213			

			(cost)=(per item)(# of items) + (start up cost)			
15	v=v(sub0) +at	18	c=.3x+3.5			
	28=v(sub0)+a(4)		r=.5x			
	43=v(sub0)+a(7)		(revenue)=(revenue per item)(# of items)			
			State break-even point. When does r=c?			
						
19	(supply)					
	S=.3p+3					
	D=-.5p+9					
	(demand)					
	State equilibrium price, price when s=d.					
==============
10/30/07
10/30/2007 blue ================
Do now.  Quick quiz.
Solve w/o cheating.
1. 
4x +3y = -12  
-2x -y = 4

2. 
4x +3y = -12  
-8x - 6y = 4


 
10/29 Monday	Cramers Rule & word problems	pg 132-134:  1,3,5,7,9,15,19;		
10/30 Tuesday	Cramers Rule & word problems	pg 132-134:  1,3,5,7,9,15,19;		
10/31 Wednesday	half-planes & simplex graphically	pg 138-9: orals, 1-45 odd		
11/1  Thursday	TEST			
11/2  Friday	word problems	pg 132-134:  2,4,6,8,10,12,18		
11/5  Monday	Matrix computation			
11/6  Tuesday	NO SCHOOL			
* solve a system by linear combination, 
  Cramer's Rule, substitution, calculator program
* run calculator program
* graph half-planes
* write system of equation for given problem



Solve by substitution is really, " Plug it in. Plug it in."

If     
Ax +By = C 
Dx +Ey = F 
     then        CE-BF 
           x=  ----------------
 	 AE-BD 
     and  
	   AF-CD 
            y = -----------------
 	   AE-BD 
 Write the array of coefficients and constants.

A B C
D E F

Note the cefficient array:
A B
D E

array
matrix - a storage thing organized in rows & columns
determinant - computation wating to be done.
(de)(ter)-(min)(ant)

State the determinant of coefficients,
compute, use this as the denominator.

  |A B |
  |D E | = AE - DB
To solve a system by Cramer's Rule:
1st.  State the determinant of coefficients,
compute, D, use this as the denominator.

2nd. Get the numerators, Dx and Dy, by writing
 new determinants using the constants instead 
of the coefficients for the variable you are solving.

3rd. Reduce the fractions.

4th. Usually write the solution as an 
  ordered pair or triple.

undefined - the compution can't be done
       This is used with expressions.
no solution -  the equation can't be solved.
       Mathematically it informs the reader that
the method was used and the math 
showed that the is no possible answer.
SEE PRIOR WORK ON SYSTEMS FROM 10/29/07
==============
10/31/2007 blue ================
	Do now.  Quick quiz. - 12 points	© 10/31/2007, A. Azzolino

	Solve w/o calculator by the method indicated. Show work.
	Circle answers.  Circled answers should include these appropriate replies: 
	"no solution," 
	"____" (the specific unique solution), 
	"many solutions including  ___."

1.   By substitution. 
	2x - 4y = 2  
	x = 3y+2

2.   By inspection (if possible).
	4x +3y = -12  
	-8x - 6y = 24

3.  By linear combination.
	3x + 2y = 26
	2x +  y  = 10

4.  She earns $26 by selling 3 red boxes and 4 blue boxes.  He earns $19 by selling 2 red boxes and 3 blue boxes.  State the prices of the red box and the blue box.

5.  The linear systems solver calculator program yields these results and crashes.
	4
	8
	0
    What answer do you write as an answer on the test?

6. By graphic solution.
	y = - 4x + 4
	x - y = 1

Test topics:
* solve a system graphically
* solve a system by inspection 
		(just looking at the equations)
* solve a system by substitution 		
* solve a system by linear combination, 
* solve a system by Cramer's Rule	
* solve a system by calculator program
* run calculator program			
* write system of equation for given problem		
?* graph half-planes
SEE 10/29/07 SYSTEMS WORK

Solve by substitution is really, " Plug it in. Plug it in."

If     
Ax +By = C 
Dx +Ey = F 
     then        CE-BF 
           x=  ----------------
 	 AE-BD 
     and  
	   AF-CD 
            y = -----------------
 	   AE-BD 
 Write the array of coefficients and constants.

A B C
D E F

Note the cefficient array:
A B
D E

array
matrix - a storage thing organized in rows & columns
determinant - computation wating to be done.
(de)(ter)-(min)(ant)

State the determinant of coefficients,
compute, use this as the denominator.

  |A B |
  |D E | = AE - DB
To solve a system by Cramer's Rule:
1st.  State the determinant of coefficients,
compute, D, use this as the denominator.

2nd. Get the numerators, Dx and Dy, by writing
 new determinants using the constants instead 
of the coefficients for the variable you are solving.

3rd. Reduce the fractions.

4th. Usually write the solution as an 
  ordered pair or triple.

undefined - the compution can't be done
       This is used with expressions.
no solution -  the equation can't be solved.
       Mathematically it informs the reader that
the method was used and the math 
showed that the is no possible answer.




==============
10/31/07	Do now.  Quick quiz. - 12 points	© 10/31/2007, A. Azzolino
Solve w/o calculator by the method indicated. Show work.
Circle answers.  Circled answers should include these appropriate replies: 
	"no solution," 
	"____" (the specific unique solution), 
	"many solutions including  ___."
1.   By substitution. 
	2x - 4y = 2  
	x = 3x+2
2.   By inspection (if possible).
	4x +3y = -12  
	-8x - 6y = 24
3.  By linear combination.
	3x + 2y = 26
	2x +  y  = 10
4.  She earns $26 by selling 3 red boxes and 4 blue boxes.  He earns $19 by selling 2 red boxes and 3 blue boxes.   State the prices of the red box and the blue box.
5.  The linear systems solver calculator program yields these results and crashes.
	4
	8
	0
What answer do you write as an answer on the test?6. By graphic solution.
	y = - 4x + 4
	3x + y = 2
Test topics:
* solve a system graphically
* solve a system by inspection 	(just looking at the equations)
* solve a system by substitution 		
* solve a system by linear combination, 
* solve a system by Cramer's Rule	
* solve a system by calculator program
* run calculator program			
* write system of equation for given problem
==========================
11/5 Monday
* solve a system by Cramer's Rule		
	pg 796: read then do 1-17 odd
* evaluate a 2x2 or 3x3 determinant by traditional method and by minors
* state properties of determinants		
	pg799: copy, pg 800: 1-11 odd
11/6 Tuesday	NO SCHOOL		
11/7 Wednesday	
* graph a half-plane		
	pg 136: 1-45, odd
11/8 Thursday	
* solve a system of inequalities by simplex method		
	pg 159:- read take notes pg160: 1, 3, 5
11/2  Friday	
* solve a 3 unknown system by Cramer's Rule		
	pg: 804: 1- 19 odd
===========================
11/8/07
12:43 PM 11/8/2007========= red
The 5 Properties of Determinants are
1. The determinant equals 0
if every element of a row or a column is 0.
    In evaluating the determinant by minors, choose that row or column to create the minors.

2. The determinant is equals 0
if two rows or two columns are identical.
    In evaluating the determinant by minors, choose the non-equal row or column to create the minors.

3. The determinant is equal its opposite
if you exchange the position or two rows or of two columns.

4. The product of a determinant and a constant is the same as the determinant
in which one row or one column was multiplied by that constant.
    In evaluating the product determinant, the changed row might be considered the coefficents of the minors used to evaluate the determinant.

5. The determinant does not change in value
if one row (or column) is picked, multiplied by a constant then added to a second row (or column), then placed in the position of the second row (or column).
==========================

==========================
11/13/07   November 13, 2007	  	© 2007, A. Azzolino

Solve:
	1x	-3y	-2z =	9			
	3x	2y	6z =	20
	4x	-1y	3x =	25										

	x	y	z	constant									
	1	-3	-2	9										
	3	2	6	20										
	4	-1	3	25										
							diagonal products									
	| 9	-3	-2|		SUMS		(ups)-(downs)		
	| 20	2	6|		54	-450	40	-356		determinant		solution
x = 	| 25	-1	3|	=	-100	-54	-180	-334	 = 	-22		 = 	2
	_____________________		________________________________		___				
	|1	-3	-2|					SUMS		-11		
	|3	2	6 |		6	-72	6	-60		
	|4	-1	3|		-16	-6	-27	-49						
																
	|1	-3	  9|					SUMS			
	|3	2	20|		50	-240	-27	-217				
z= 	|4	-1	25|		72	-20	-225	-173	 = 	-44		= 	4
	_____________________		________________________________		___				
										-11		
		D

		
	|1	9	-2|					SUMS					
	|3	20	 6|		60	216	-150	126				
y =	|4	25	 3|		-160	150	81	71	 = 	55		= 	-5
	_____________________		________________________________		___				
										-11		
		D

=================
11/13/07	 November 15, 2007	  	© 2007, A. Azzolino
Complete.
1.  The determinant equals 0 if ___.
  
2.  The determinant equals 0 if ___.
  
3.  The determinant equals ___ if you exchange the position or two rows or of two columns. 
  
4.  If one row or one column of a determinant is multiplied by that constant, the changed determinant _____
  
5. The determinant does not change in value If SOME row (or column) is picked, multiplied by a constant then added to a DIFFERENT row (or column), and this is then placed in the position of the __ row (or column). 
  
Simplify with thought, not major computation.
6.
| 4	-2	-2|
|5	2	2| = _____
| b	-1	-1|

.
| 0	-2	-1|
| 0	10	30| = _______
| 0	-1	  3|

 Transform as directed.
8.
| 1	-2	-1|         -2R3 + R1
| 2	1	3|           ------------->
| 0	-1	4|	         R1

Multiply if multiplication is permitted.  A = [ 1 2 3 ]     B = [ [1]  [2]  [4] ]	C= [ 1 1 ] [ 2 1 ] [ 4 2 ] ]
9.   AB	10.   BC	11.  AC
=======================
11/14/2007 red 
* solve a system by Cramer's Rule
* evaluate a 2x2 or 3x3 determinant 
	by traditional method and by minors
* state properties of determinants
* graph a half-plane
* solve a system of inequalities by simplex method
* reviewd vocabulary including dimension, element
	row column, square matrix, 0 matrix, closure
* add, subract matrices when possible
*  2nd ENTRY to redo last command
===========   
thurs	11/15/2007

The 5 Properties of Determinants are listed on pages 798 and 799 of your text or stated below. 
1. The determinant equals 0 
if every element of a row or a column is 0. 
  
2. The determinant equals 0 
if two rows or two columns are identical. 

3. The determinant equals its opposite if you exchange the position or two rows or of two columns. 
  
4. The product of a determinant and a constant is the same as the determinant 
in which one row or one column was multiplied by that constant. 

5. The determinant does not change in value 
if one row (or column) is picked, multiplied by a constant 
then added to a second row (or column), then 
placed in the position of the second row (or column). 

Evaluate determinant on a hhc.  
1  Create a matrix.	
2  [MATRIX] [MATH] 1: det( [ENTER]	
3  On home screen write the determinant name
	det([A]	[ENTER]

To add/subtract matices : component wise on conforming matrices.
To multiply matices:
1st	Determine if matrices may be multiplied
	Arow,column matches only Brow,column   where the row of A equals the column of B
2nd	Determine dimensions of the product matrix. component wise on conforming matrices.
	Product AB has dimension row of A, column of B
3rd	Each product element is the sum of products of (row)(column) of factor matrices.
	
To multiply add, subtract matrices on determinant.
1.	Store matrices.
2.	Use  + - x / on calculator face or [MATRIX][MATH] for other functions.

-3	-2	9
2	6	20
-1	3	25
	(2,-5,4)	
=======================
11/19/2007
* solve a system by Cramer's Rule
* evaluate a 2x2 or 3x3 determinant 
	by traditional method and by minors
* state properties of determinants
* graph a half-plane
* solve a system of inequalities by simplex method
* reviewd vocabulary including dimension, element
	row column, square matrix, 0 matrix, closure
* add, subract matrices when possible
*  2nd ENTRY to redo last command
=======================
11/27/2007 blue 
1.  Use your calculator to state the inverse of 
[[ 2  1  -1]
 [ 1  1  1  ]
 [ 1  2  1  ]]

2. With paper, multiply:  

[the inverse from question 1]*[[2 ][7][4]]


3. Show teacher answer.

4.  Copy:

      [A]*[X] = [B]

             [X] = inv([A])*[B]

5.  Solve system on your calculator.

 2x +y -z = 2
   x +y + z= 7
   x + 2y + z = 4



[[5][-3][5]] see pg 804

hw pg 808 test
       pg 786/  by calculator and augmented

5,-1,4	-2,3,4	1,-2,4
-4,2,1	-1,2,3	2,5,-3
=======================
11/28/2007 blue 
1.  Use your calculator to state the inverse of 
[[ 2  1  -1]
 [ 1  1  1  ]
 [ 1  2  1  ]]

2. With paper, multiply:  

[the inverse from question 1]*[[2 ][7][4]]


3. Show teacher answer.

4.  Copy:

      [A]*[X] = [B]

             [X] = inv([A])*[B]

5.  Solve system on your calculator.

 2x +y -z = 2
   x +y + z= 7
   x + 2y + z = 4


[[5][-3][5]] see pg 804

hw pg 808 test
       pg 786/  by calculator and augmented

5,-1,4	-2,3,4	1,-2,4
-4,2,1	-1,2,3	2,5,-3
=======================
======== red  12/4====
Graph:
1. y>0
2. x > or = to 0
3. y < or = to -2x+4
4. y < x + 1
5. pg 159, 160

Hw collect a2q67, a2q68
begin a2q102
Hw graph pg 159-160
x + 3y <= 100
120x + 90y <= 9000
x + 2y <= 200
x + 6y <= 160
x>= 0
y>=0


y <= -1x/3 + 100/3
120x + 90y <= 9000
 y<= -120x/90 + 900/90
  y<= -4x/3 + 100


x + 2y <= 200
x + 6y <= 160
x>= 0
y>=0


R= 265x + 365y
x + 3y <= 100
120x + 90y <= 9000
x + 2y <= 200
x + 6y <= 160
x>= 0
y>=0

======================
12/5/2007  ========= blue  ===========
Graph:
1. y>0
2. x > or = to 0
3. y < or = to -2x+4
4. y < x + 1



5. pg 159, 160
4x/3+100
x + 3y <= 100
120x + 90y <= 9000
x + 2y <= 200
x + 6y <= 160
x>= 0
y>=0


y <= -1x/3 + 100/3
y<= -120x/90 + 900/90
y<= -4x/3 + 100
y<=-x/2+100
y<=-x/6+80/3
x>= 0
y>=0

Xmin= -5
Xmax=205
Xscl=50
Ymin=-5
Ymax=120
Yscl=50
Xres=1

Graph:
1. y>0
2. x > or = to 0
3. y < or = to -2x+4
4. y < x + 1
5. pg 159, 160

Hw collect a2q67, a2q68
begin a2q102
Hw graph pg 159-160
x + 3y <= 100
120x + 90y <= 9000
x + 2y <= 200
x + 6y <= 160
x>= 0
y>=0


y <= -1x/3 + 100/3
 y<= -4x/3 + 100


x + 2y <= 200
x + 6y <= 160
x>= 0
y>=0

Solve by linear programming
R= 265x + 365y	objective function
x + 3y <= 100	constraint	
120x + 90y <= 9000	constraint
x + 2y <= 200	constraint
x + 6y <= 160	constraint
x>= 0		constraint	y>=0		constraint
shaded region	feasible region
vertices of feas. reg	max & min values	
vertex
x	y
0	0	R= 265x + 365y
0	26 2/3
40	20
66 2/3	11 1/9
75	0	

Minimize z.
z = 5x + 7y with constraints of:
x>= 0
y>= 0
2x+3y >=6
3x-y <= 15
-x + y <= 4
2x + 5y <= 27

pg 615, ex 2, Larson PRECALC
 0,2
=======================
12/7/2007  red  
DO NOW:	Graph:
1. y = x		2. y = -x
3. y = 1/x		4.  y = x^2
* reviewed test
* quiz
=======================
12/11/2007  blue === no red ====

x, the identity function
-x, the opposite function
1/x, the reciprocal function
x^2, the squaring function

*state the laws of exponents	
*point-plot and name functions	
*complete monomial, polynomial computation	
*list properties of functions	
		
·Review polynomial vocabulary on pg 167. 		
·Simplify, add,subtract polynomials. 		
·Solve term-dependent equations. 
    pg 170/ 1, 7, 9, 15, 17, 19, 23, 25 		
·State the laws of expenents regarding multiplication and raising to a power. 		
·Multiply monomials. Raise monomials to a power. Distribute. Solve equations with the same base. 
    pg 172/orals, 173/1-34 odd, 35-38, all 		
·Multiply polynomials by "long multiplication" and mentally and with written expension by FOIL. 		
·Note special products: difference of 2 squares and perfect trinomial square. 175/orals, 175/1-56 odd 		

From HW:
Graph:
1. y = x		2. y = -x
3. y = 1/x		4.  y = x^2
=======================
12/12/2007 ========= blue  ===========
DO NOW:
1. Graph the opposite of the reciprocal of a number

*state the laws of exponents	
*point-plot and name functions
*complete monomial, polynomial computation	
*list properties of functions
	
·Review polynomial vocabulary on pg 167. 	
·Simplify, add,subtract polynomials. 	
·Solve term-dependent equations. 
     pg 170/ 1, 7, 9, 15, 17, 19, 23, 25 	
·State the laws of expenents regarding 
     multiplication and raising to a power. 	
·Multiply monomials. Raise monomials to a power.   
    Distribute. Solve equations with the same base. 
    pg 172/orals, 173/1-34 odd, 35-38, all 	
·Multiply polynomials by "long multiplication" and mentally and 
   with written expension by FOIL. 	
·Note special products: difference of 2 squares 
   and perfect trinomial square. 
   175/orals, 175/1-56 odd 
========================
12/13/2007 	DO NOW:
1. Graph the reciprocal of 2 more than a number.
2. Graph 2 more than the reciprocal of a number

Copy the laws at the right.
SEE PAGE http://www.mathnstuff.com/math/spoken/here/2class/210/laws.htm & 
pg 171 172, 216, 212

*state the laws of exponents	
*point-plot and name functions
*complete monomial, polynomial computation	
*list properties of functions
=======================
12/14/2007  red
laws of exponents
x^(-y) in particular

think of 3^2 / 3^3

3^2 / 3^4 is 

1 / 5^(-2) is
pg 212-213
=======================
12/17/2007 BLUE
   Review now for a 2 question quiz on graphing functions.  You will put the quiz on the same paper as your last graphing quiz.
  Think point-plotting with out a calculator.
  Review the identity, opposite, squaring, and reciprocal functions.  Remember the word 
asymptote and to make an asymptote with a 
dashed curve, usually a dashed line.

TAKE A TWO QUESTION QUIZ NOW.
1. Graph two more than the reciprocal of a number.
2. Graph the reciprocal of two more than a number.


Continue use and review of the 
LAWS OF EXPONENTS.
laws of exponents
x^(-y) in particular

think of 3^2 / 3^3

3^2 / 3^4 is 

1 / 5^(-2) is
pg 212-213
=======================
12/18/2007  BLUE
Hand in homework.
 Review now for a 2 question quiz on graphing functions.  You will put the quiz on the same paper as your last graphing quiz.
 Think point-plotting with out a calculator.
 Review the identity, opposite, squaring, and reciprocal functions.  Remember the word asymptote and to make an asymptote with a 
dashed curve, usually a dashed line.

TAKE A TWO QUESTION QUIZ NOW.
1. Graph 2 less than the reciprocal of a number.
2. Graph 2 less than the square of a number.
Then study notes from last week & complete a second quiz.

Complete statements of the LAWS OF EXPONENTS.
1. When you multiply two numbers, you ______ the base and _______ the exponents.
2. When you divide two numbers,  you ______ the base and _______ the exponents.
3. When you raise a number to a power,  you ______ the base and _______ the exponents.
4. When you take a root,  you _____ the base and ______ the _____ of the ______ by the  _______.
5. x^a + x^b = _________________, if a does not equal b.
6. x^a - x^b = _________________, if a does not equal b.

Be sure you have pg 212-213 completed and also pg 171-173.

laws of exponents
x^(-y) in particular
think of 3^2 / 3^3
3^2 / 3^4 is 
1 / 5^(-2) is
=======================
12/20/2007  blue 
be sure you get the home work sheets.
test on Dec 26th!
1.Graph three less than the square of a number.
2Graph one less than the opposite of the reciprocal
of a number
3. Simplify. Circle answer.

a.  (3x^2y)(-4x^2y^3)		b.  (3x^2y^5)^2

c.  (x^(h + k))^2(x^(h - k))	d. (x^2y^5) ÷ (x^(-2)y^3))	

4.Graph the reciprocal of 3 more than a number.
=======================
12/20/2007   red 
1.Graph three less than the square of a number.
2Graph one less than the opposite of the reciprocal
of a number
3. Simplify. Circle answer.

a.  (3x^2y)(-4x^2y^3)		b.  (3x^2y^5)^2

c.  (x^(h + k))^2(x^(h - k))	d. (x^2y^5) ÷ (x^(-2)y^3))	
4.Graph the reciprocal of 3 more than a number.
=======================
12/21/2007  red ==========
12/7/2007, 12/11/2007  Graph:
1. x, the identity function	
2. -x, the opposite function
3. 1/x, the reciprocal function
4. x^2, the squaring function
12/13/2007 Graph:
1. x, the identity function	
2. -x, the opposite function
3. 1/x, the reciprocal function
4. x^2, the squaring function
5. the opposite of the reciprocal of a number
6. the reciprocal of 2 more than a number.
7. 2 more than the reciprocal of a number
8. the opposite of the reciprocal, -1/x

12/20/2007 Graph:
9. three less than the square of a number.

=======================
12/24/2007 =====  RED =====
*solve	*simplify

pg 181  / 1-9, 11, 12, 24, 25, 29-33
=======================
dec 26/ 07 	Determinants, Matrix Test © 12/3/2007, A²
Show work for possible partial credit. Circle answer.
1. State the Zero matrix of dimension 2x3.		
2. State the Identity matrix of dimension 2x2.
3. Simplify 3 [[ 2   4]  + [[-3 6]
                        [ 0   -1]]     [4 2]]
4. Multiply. [[1  0 -2 ] ? [[0 ]
	         [3  0 0 ]      [1 ]
	         [-2 0 5 ]]     [4 ]
5. Simplify. Circle answer.			
  |1  0 |
  |3  3 |
6. Solve by Matrices.
- 1x + y + 2z = 8
 2x  -  y + 2z  = 4
           y + z    = 2
7. Solve by Cramer’s Rule. 		
- 1x + y + 2z = 8
 2x  -  y + 2z = 4
           y + z  = 2
=======================
12/27/2007 =====  RED =====
asquared@mathnstuff.com

domain = kingdom of the x, 
THE X VALUES YOU MAY USE IN THE FUNCTION

range = how far the y can go
THE Y VALUES YOU GET WHEN A FUNCTION IS USED
* ORIGINAL 1-4, 9 and root fx on TI
 
12/27/2007 == blue ===
asquared@mathnstuff.com
* QB questions, chapter 4

domain = the kingdom of the x
THE VALUES ONE MAY USE IN THE FUNCTIONS

range = how far the y can go
THE VALUES GENERATED BY THE FUNCTION
=======================
1/2/2008  red ============
pg 175, 185, 191, 196-197

function - a correspondence between 2 sets.
assigns each element/member of D, the domain, EXACTLY ONE member of R, the range.


conic sections
function
vertical line test
f(x) read as "f of x"

f(x) the function
- f(x) the opposite of the function
f(-x)
-f(-x)



3:22 PM 1/2/2008 == blue ===
pg 175, 185, 191, 196-197

function - a correspondence between 2 sets.
assigns each element/member of D, the domain, EXACTLY ONE member of R, the range.


conic sections
function
vertical line test
f(x) read as "f of x"

f(x) the function
- f(x) the opposite of the function
f(-x)
-f(-x)
=======================
12:42 PM 1/3/2008  ========= red  blue

Given graph of f(x), Graph -f(x) and f(-x)
x^3 (x

Simplify exponential expressions.
Expand:
(x+2y)^2  = x^2 + 4xy + 4y^2
(x - 3a^2)^2 = x^2 - 6xa^2 + 9a^4
(2+x)^2 =


(x+y)^0
(x+y)^1
(x+y)^2
(x+y)^3

=======================
CRAMER'S RULE SPREADSHEET
www.mathnstuff.com/math/xls/cramers.xls

MATRIX SPREADSHEET
www.mathnstuff.com/math/xls/maytrix.xls

SYNTHETIC DIVISION SPREADSHEET
the synthetic divison page of 
www.mathnstuff.com/math/xls/poly.xls