September 21, 2007 Class Notes

September 21, 2007
*We went over homework*
*NOTE: Timeliness has been added to the blog rubric and a link to WIKI has been added to the page to access handouts*

-Absolute Value Inequalities
Equations: x=# x=(+#) or (-#)
Case 1
x># x>(+#) or x<(-#) EX: x>2
x>2 or x<-2 Case 2
x<# x<(+#) or x>(-#)
EX: x<2>-2

*And vs Or*
Less than--->and
-less thand
Greater than--->or
-Greator than

Application
3x-2 ≤ 1
3x-2 ≤ 1 3x-2 ≥1
x ≤ 1 and x ≥ 1/3

-Interval Notation
-Third way to depict inequality answers
-Easier way/less time consuming
[ ] ----≤ ≥

( ) ----< >
EX: 3x-2≤1 [1/3, 1]
EX: x >2 (∞, -2)∪(2, ∞)

·means union to connect two sets together

-Inequalities by Calculator
EX: (x+3)/(x-2)> 0 *Enter left side in Y1
*Start with standard window
* Answers above the x axis
* ( -∞,1) ∪(2,∞)

*Homework quizzes returned*Use homework quizzes to show your areas of weakness and to gauge where you are in understanding*

-Functions –“last thing before we jump into trig waters”-Mr. M
*Operations and functions
-arithmetic EX: f(x)=x2-4
f(x)+g(x) g(x)=x+3
f(x)-g(x) (f+g)(x)=f(x)+g(x)
f(x) (f+g)(x)=x^2-4+x+3
-composition = x^2+x-1
(fog)(x)
*cont’d on Tuesday, September 25th*
*Homework: Pg 168 #29-59/odd, 63, 65, Pg 179 #1-9/odd*

*Alright hope everyones weekend went well, see ya'll tomorrow!*

-Lauren

Well I'm finally posting my notes from two weeks ago

So here they are. Just double-click the pictures to get a bigger picture of the notes

Homework
Pg 155 #21-27 odd, 53-69 odd, 73, 76, 77

9/18/07 How to pick a method

How to pick a method:
-What characteristics do we use to solve an equation?
-When is it more efficient to us one method over another?


An important side note: For the quiz coming up tomorrow make sure you know how to use each of these methods, and be able to tell why you used the method to solve the problem. Absolute value:
X= 5 for this equation x= 5 or -5
X-3= 5 we are trying to find a way to make this 5, -5
-So what you would need to do is eliminate the absolute value signs, and it will look like this:
X-3= 5 or X-3= -5 so X would be 8 or -2
-You want to get the absolute value alone like you would get a(2) alone
X2+X-6= 4 or X2+X-6= -4 X2+X-10= 0 or X2+X-2= 4
So X=-2,1 or (X+2) (X-1)
If you plugged this into the quadratic it would look like this: -1+/-√1-4(1)(-10)/2

which would equal: -1+/-√41/2 (You could also check your answer graphically.)


Radicals:
(√X-4) 2 =(6) 2 (√X+8) 2 =(X+2) 2
X=40 X-4= 36 X+8= (X+2) 2
X+8= X2 +4x+4
0= X2 +3x+4
(X+4) (X-1)

We have to make sure they both work . 1 would be the actual solution because when you plug -4 back into the original equation it equals 2 and -2
X≠4 X=1

More difficult example:
√X +√2x =4 -make sure you isolate one of the radicals
(√2x) 2 = (4-√x) 2
2x= (4-√x) 2
2x= 16- 8√x +x -divide the whole equation by negative 8
(-1/8 (x-16)) 2 =(√x) 2
1/64 (x2 -32x +256)= X
1/64 x2 -32/64x+ 256/x=X
X2 -32x+256 = 64x
X2 -96x+256= 0 -Use the quadratic formula to finish


Last week we also began talking about inequalities:
Inequalities: divide by (-) or multiply by (-) switch the order
- compound inequality two ways to solve

You can use either method for compound inequalities!
-3<>

x> -7 x≤ 5
-7<>

Domain


Key things to look at when finding domain with a function involving square roots.
Ø Square roots cannot be negative


Ex. Pg 132 #28
K(x)= x^2+1 set the function as an equality

X^2+1>0 anything times its self is positive so the domain of this function is all real numbers.


Ex. Pg 132 # 27
H(x)= 2-x set the function up as an equality

2-x >= 0 subtract –2 from both sides
-2 -2
-x >= -2 divide by –1 and since you are dividing by a negative the inequality sing flips
-1 -1
x <= 2

Ex. Pg 130 #25

F(x)= ` X `
X^2 * 2X factor the denominator

F(x)= ` X `
X (X-2) set the denominator equal to 0

X (X-2) =0
X=0
X-2=0
+2 +2
X=2
So X cannot equal 0 or 2 because then the denominator is 0

Key things to remember are no negatives under a radical and the denominator cannot equal 0.





Piecewise

Important thing to remember is that you find the value that the two functions share.

F(x) { radical over 1-x if x<1
X^2-1 if x>= 1 plug in 1 into both functions

Radical over 1-1=0
1^2-1=0


Homework
9/12/07
pg 155 #1-10 even, 33-42even 43-52even

You may not have figured this out yet, and I'm sorry for not telling you yet, but if you double click on the scanned notes, they ARE readable. I probably should've told you that.

Brad.

Answer to question 25, on page 116.

Ron was having a peacfully romantic dinner with his wife, Paula, yep, with candles, dimmed lights, and all that jazz. They had just finished their salad, a nice grouping of vegetables and the occasional pomagranate, for zest, as well as a rare italian vinigrette. When all of a sudden, Ron went into the kitchen to get their filet mignons. When he got these he was struck by the fact that he was missing the A1, which is served in 9 out of 10 steakhouses. Ron asked Paula were he could get A1 at this hour, Paula said that there was A1 in the local cave. Ron, in dire need for A1, which is served in 9 out of 10 steakhouses, goes to the local cave. He ventures deep into the cave when instead of A1, he finds a baracuda! With legs! Oh! What a twist! Betcha didn't see that one coming! He runs, screaming, out of the cave and escapes, unscathed. Outside the cave Ron remembers how much he needs A1, which is served in 9 out of 10 steakhouses. Ron, driven by his desire for A1, which is served in 9 out of 10 steakhouses, goes back into the cave. Once inside Ron peers deeper into the gloomy depths of the cave, and sees the A1, which is served in 9 out of 10 steakhouses. Ron grabs the bottle of A1, which is served in 9 out of 10 steakhouses, and bolts towards the entrance of the cave, only to notice that he has grabbed the cheap Canadian knock off, Eh1, which is not served in 9 out of 10 steakhouses. Ron drops the imposter and runs back to grab the real bottle of A1, which is served in 9 out of 10 steakhouses, he grips the neck of the bottle and takes off for the enterance to the cave. Ron dodges the baracuda and yells "It's served in 9 out of 10 steakhouses!" as he bolts past. Ron runs as fast as he can towards the opening at the end of the cave, Ron escapes the horrors of the local cave, with the A1, which is served in 9 out of 10 steakhouses. All of a sudden, Bill Romanowski grabs him and uses his huge, steriod enlarged, muscles to drag the screaming Ron back into the cave. Which is actually the back door the the ESPN Sports Center. OH TWIST!

You know you wanted me to post it,

Brad.

You know you wish your handwriting was as good as mine. Bragging aside, I appologize for the lateness of my entry, all of the computers in my house are acting up, seriously, I've tried to do this on five different computers. So if this works, I'll be giving a huge sigh of relief and probably listening to some Jimi Hendrix.

Notes

This picture of a graphing calculator is a more detailed description of how to find the intersection point of two equasions, step by step. It took me like thirty minutes to make this so be happy, or else. VOTE HOLLAND '08!

Page 1

Page 2

Lesson for 9/09/07

Solving Equations by Graphing

Example #1:

First step is to set the equation equal to zero.
2x^2-x-6=0 (2x^2-x-6 is y1)
Next put the equation into your calculator with a standard window to look at it.
Make sure all stat-plots are turned off
2nd—Calculate—Zero
When you arrive at the graph to make your guess make sure the left bound is on the left side of the zero.

Right Bound is anywhere on the right side of the zero, and the guess should be on the x-axis
After calculating the zero do the same thing for the left side of the parabola.
You should come out with x= -1.5 and y= 0


Example #2:
Left Side of the Equation= y1
Right Side of the Equation=y2
Enter the first part of the equation into y1 on your calculator and the second part into y2
To distinguish y1 from y2 on the graph go into the y= screen and all the way to the left of y2 hit enter to change to a thick line.
Next Go to 2nd—Calculate---Intersect---Enter---Enter
And then guess on one of the intersection points
Intersection points = (x= 2.30), (x= -2.50), (x= -1.24)


Solving Quadratic Equations

Learned Last Year:
1.) Factoring
2.) Quadratic Formula
3.) Completing the Square
4.) Extracting Square roots
5.) Graphing

We are going to talk about how each method works and when it is most effective to use each one.

Extracting Square Roots:
(2x-1)2=8
2x-1=±√8
2x=1 ± √8
x= (1 ±√8) / 2
x=(1 ± 2√2) / 2
x= ½ ± √2
Any time you have (__)2= # you will use extracting square roots


Homework:
Due 9/12/07
Pg. 142 #’s 28-38 Even
Due 9/14/07
Pg.155 #’s 1-10 Even
33-42 Even
43-52 Even

Line of best fit August 29th

Find data and enter into calculator by going to stat then press 1. Put the X-axis data into L1 and the Y-axis data into L2.

Go to stat plot by pressing 2nd then Y= and turn on number 1.

Go to window and set up a good window that the data will fit in.

Estimate a line of best fit and out the equation into the Y=.

Make the line of best fit by going into stat then moving over to calc the choose number 4.

After having the line of best fit go to catalog by pressing 2^nd then 0. Then scroll down to diagnostics and turn it on and then redo the process for the line of best fit.

The r value shows correlation. Correlation tells how close the points are to the line of best fit. The correlation is between -1 and 1. Negative numbers means that the slope is negative and if the numbers are positive then the slope is positive. The closer the r value is to 1 or -1 the closer the points are to the line. If r is 0 then there is no correlation.

HOMEWORK:

Pg 102, #1-10, 29, 31, 33 and finish the triangles sheet.