Wednesday, October 31, 2007
Identities BOB
In this unit I pretty much understood everything. The part where Mr. K was proving how the whole sine dance equations worked kind of threw me off at first. My muddiest point is proving that one side is identical to the other. I just don't know where to start sometimes. Do I change everything to sine and cosine? Do I use the Pythagorean identity to make substitutions? Do I factor? Do I multiply by 1? I guess I just have to practice a little more. Another thing is some of the questions that were on the pre-test (number 2 and 3) where you had to find the cos(a-b) and it gives you two angles, questions like that. That's... pretty much it.
BOB 2
Okay! So here's my blog for this unit, Identities. I'll say that my muddiest point is when you have to do the clever idea which is multiplying by the number 1. Everything else is pretty straight forward. I think thats it for now. Good luck to everyone on the test!
***When do we see our previous tests???***
BOB
This unit wasn't as bad as I thought it would be, but there were times where I had trouble. There are so many Identities that I am not really familiar with yet and because of this, I sometimes have trouble proving one side from the other. Other than that, I'm fine with doing the algebra. I also tend to make little concept errors such as writing in the wrong function, or not changing signs when we're supposed to leads me to have a completely different answer. Hopefully, with a little bit more practice I'll be ready for the test.
BOB
So far in this unit I think I've been able to understand most of the work we do. It's just sometimes I forget that one thing can be changed into another identity and it throws me off. Also the double angle stuff I don't really understand when and where I should and can use it. Another thing is that I also make silly like mistakes which throw my answers into oblivion. Sometimes it's just a spelling error but I also make concept errors when I think it's right. Hopefully I'll be able to grasp everything that I've been missing and I'll try not to make little mistakes anymore. Good Luck to everyone on the test.
BOB
Another BOB, another upcoming test.
The trigonometric identities unit hasn't been too devastating. I'm grasping the concept of proving little by little. Although I do have an issue with all the corrolories and remembering that everything can be written as something else, but I'm working on that.
My issue is with the number one and how it can be written in many endless ways. Going through with proving identies, I always forget that the identity can be written in a different way or I can change it to make it look another way.
I understand sum and difference identies, but I always have to watch out for the "signs" because it will just lead me in the wrong direction, but I'm working my issues out slowly.
I do understand what is going on, but the problem lies with having to apply everything to the questions. Like Mr. K said, there are so many different ways that students can solve the identities. We'll see how the test goes and I hope I don't do too badly.
Good luck everyone.
(I wonder when we get to see our previous tests?)
The trigonometric identities unit hasn't been too devastating. I'm grasping the concept of proving little by little. Although I do have an issue with all the corrolories and remembering that everything can be written as something else, but I'm working on that.
My issue is with the number one and how it can be written in many endless ways. Going through with proving identies, I always forget that the identity can be written in a different way or I can change it to make it look another way.
I understand sum and difference identies, but I always have to watch out for the "signs" because it will just lead me in the wrong direction, but I'm working my issues out slowly.
I do understand what is going on, but the problem lies with having to apply everything to the questions. Like Mr. K said, there are so many different ways that students can solve the identities. We'll see how the test goes and I hope I don't do too badly.
Good luck everyone.
(I wonder when we get to see our previous tests?)
BOB
I think this unit about Trig Identities was a hard one to grasp. There are a lot of identities that i haven't recognized yet, but I'll be sure to get them down in time for the test. The thing I'm most concerned about is my algebra. I tend to make minor mistakes whenever proving an identity. That's all I really need to clear up though. Everything else, I hope, will all get better with more practice.
BOB
Hello! It is roslyn. This unit was very hard, well except for the proving part. I found that very easy. The other trigonometric identities were very hard. I liked how we got into groups and went over the problems that we had problems with. It was fun and very educational. But anyways, overrall I hope I do good on the test!
Halloween Scribe Post - New Unit: Exponents
Today's class, we were divided into groups and started off solving for "x" given 2-cosx = 2sin^2x
I started off with changing the sin^2x into 1-cos^2x, then multiply it by 2. The moved everything onto the left side, getting 2cos^2x - cosx = 0. Then factor cosx out of it which you'll then get cosx(2cosx -1) = 0. From there you can tell that cosx = 0 and cosx = 1/2 which means x = pi/2, 3pi/2 and x = pi/3 and 5pi/3.
We were then introduced to the new unit; only a very light introduction. We were asked to express the numbers 2, 3, 4/9, and 1/4 in the the forms of exponents. For example, 2 can be express as 4^(1/2), 3 can be expressed as 6561^(1/8), 4/9 can be expressed as (16/81)^(1/2) and 1/4 can be expressed as 2^(-2). You can also give numbers negative exponents, which you would then have to turn the base of the number into it's reciprocal. For example; 4^(1/2) can also be expressed as (1/4)^(-1/2). Notice the base of the number that was previously 4, became 1/4 and the exponent of 1/2 became -1/2. We were then asked to express 1/4 in 10 other ways for tomorrow's class.
Afterwards, we got a little deeper into the subject; now having to find the exponents in the given equation 2^x = 64. That one was a no brainer. But then there was 27^(2x-1) = 3. The way you solve that is to rewrite the equation with both sides of the equal sign having the same base number; for example 27 = 3^3, then you have the base number of 3 on both sides. So (3^3)^(2x-1) = 3^1. You then take the exponents alone, (3)(2x-1) = 1 **note that the "3" in that is the exponent not the base, and the "1" is from the right side of the equation because 3 is the same thing as 3^1**. Then you simply solve for "x";;
3(2x-1) = 1
6x - 3 = 1
6x = 4
x = 4/6 or 2/3
So there you have solved for "x" in the equation 27^(2x-1) = 3
We were also given in the set, 3^x = 1/27. Remembering that negative exponents give you recipricols, the answer must be (-3).
Lastly, we were given this set to solve for x:
4^(1-x) = 8 49^(x-2) = 7 √7 25^2x = 5^(x+6)
the answers are as follows:
4^(1-x) = 8 (2^2)^(1-x) = 2^3
(2)(1-x) = 3
2 - 2x = 3
2x = -1
x = =1/2
49^(x-2) = 7 √7
(7^2)^(x-2) = (7^1)(7^(1/2))
(7^2)^(x-2) = 7^(3/2)
(2)(x-2) = (3/2)
2x - 4 = 3/2
2x = 4 + 3/2
x = 11/4
25^2x = 5^(x+6)
(5^2)^(2x) = 5^(x+6)
(2)(2x) = x+6
3x = 6
x = 2
And that was everything that we covered in Halloween's class, that I'm surprised everyone showed up to. Tomorrow's scribe can be Sergio, he can cover All Saints Day's class for everyone.
I started off with changing the sin^2x into 1-cos^2x, then multiply it by 2. The moved everything onto the left side, getting 2cos^2x - cosx = 0. Then factor cosx out of it which you'll then get cosx(2cosx -1) = 0. From there you can tell that cosx = 0 and cosx = 1/2 which means x = pi/2, 3pi/2 and x = pi/3 and 5pi/3.
We were then introduced to the new unit; only a very light introduction. We were asked to express the numbers 2, 3, 4/9, and 1/4 in the the forms of exponents. For example, 2 can be express as 4^(1/2), 3 can be expressed as 6561^(1/8), 4/9 can be expressed as (16/81)^(1/2) and 1/4 can be expressed as 2^(-2). You can also give numbers negative exponents, which you would then have to turn the base of the number into it's reciprocal. For example; 4^(1/2) can also be expressed as (1/4)^(-1/2). Notice the base of the number that was previously 4, became 1/4 and the exponent of 1/2 became -1/2. We were then asked to express 1/4 in 10 other ways for tomorrow's class.
Afterwards, we got a little deeper into the subject; now having to find the exponents in the given equation 2^x = 64. That one was a no brainer. But then there was 27^(2x-1) = 3. The way you solve that is to rewrite the equation with both sides of the equal sign having the same base number; for example 27 = 3^3, then you have the base number of 3 on both sides. So (3^3)^(2x-1) = 3^1. You then take the exponents alone, (3)(2x-1) = 1 **note that the "3" in that is the exponent not the base, and the "1" is from the right side of the equation because 3 is the same thing as 3^1**. Then you simply solve for "x";;
3(2x-1) = 1
6x - 3 = 1
6x = 4
x = 4/6 or 2/3
So there you have solved for "x" in the equation 27^(2x-1) = 3
We were also given in the set, 3^x = 1/27. Remembering that negative exponents give you recipricols, the answer must be (-3).
Lastly, we were given this set to solve for x:
4^(1-x) = 8 49^(x-2) = 7 √7 25^2x = 5^(x+6)
the answers are as follows:
4^(1-x) = 8 (2^2)^(1-x) = 2^3
(2)(1-x) = 3
2 - 2x = 3
2x = -1
x = =1/2
49^(x-2) = 7 √7
(7^2)^(x-2) = (7^1)(7^(1/2))
(7^2)^(x-2) = 7^(3/2)
(2)(x-2) = (3/2)
2x - 4 = 3/2
2x = 4 + 3/2
x = 11/4
25^2x = 5^(x+6)
(5^2)^(2x) = 5^(x+6)
(2)(2x) = x+6
3x = 6
x = 2
And that was everything that we covered in Halloween's class, that I'm surprised everyone showed up to. Tomorrow's scribe can be Sergio, he can cover All Saints Day's class for everyone.
Meeelar's Flickr Assignment
Im having trouble uploading my picture to the blog. So heres there link to it on Flickr.
Tuesday, October 30, 2007
B0Bb`n itttt again!
Trig identities has to be my muddiest point. Another problem is, I'm not even sure what it is about it that I don't get, so I don't know what I need to work on. I'm not sure if it's remembering how to work out the trig identities or not. Kinda complicating. Mmm.. don't think there's much more I have trouble with. Oh.. one last thing is that there's a several questions I've been meaning to ask Mr. K about exercise 16, but haven't got the time to ask in class. So HELP MEEEEEEEE PLEASE, after lunch preferably, if you read this Mr. K. =D
Flickr Assignment
I'm so frustrated with it because it's not showing up in the searches and I did everything ages ago (creating the account and the five pictures).
Anyway, here's my Flickr assignment.
Hello, everyone. Today we had two math classes, in the morning and in the afternoon. The morning class was spent on a pre-test and the afternoon there was a quiz...
The pre-test contain eight questions..
1) Simplify: sin(2x+π)
A. sin2x
B. cos2x
C. -sin2x
D. -cos2x
The answer is C because sin(2x+π) is similar to sin(α+β) and the equation for this is simple, just do the sine dance!
sin(α+β)=sinαcosβ+cosαsinβ .. now you just plug sin(2x+π) into the equation
sin(2x+π)=sin2xcosπ+cos2xsinπ
sin(2x+π)=sin2x(-1)+cos2x(0)
sin(2x+π)=-sin2x+0
sin(2x+π)=-sin2x
cos π= -1
sinπ= 0 anything multiplied by 0 equals 0 so the right side reduces..
2) The terminal arm of an angle Ө in standard position passes through point (m,n) where m>0, n>0. Determine the value of sin(π+Ө).
A. ( -n)/√(m^2+n^2)
B. ( -m)/√(m^2+n^2)
C. ( n)/√(m^2+n^2)
D. ( m)/√(m^2+n^2)
The answer is A.
The question says that m and n are both positive so you know the coordinates are in the first quadrant.
m=x coordinates
n=y coordinates
Ө= angle
Once you draw a diagram you can use the pythagorean theorem to find the hypotunse, which is √(m^2+n^2).
Since sin=Opposite/adjacent then..
n/√(m^2+n^2)
BUT... it asks for the value of sin(π+Ө) so you substitute it in the sin(α+β)=sinαcosβ+cosαsinβ when you finish you get -sinӨ. Soo.. you multiply everything by -1.
And your answer is
-n/√(m^2+n^2).
Question# 3.
In this slide mr.k drew a diagram of cos A and you realize that the sin of this triangle is the sin of sin B... this means that both A and B are the same angle. The question is asking for the value of cos (A-B) and since A and B are the same the answer will be zero!
cos(A-B) = cos 0
= 1 < the answer is one because 1 is the raduis always 1 in the unit circle.
Question #4.
In this slide instead of having 2cos^2x+cosx-1=0 we let cosx=A so it's easier to read...
after we factored it to find the values of A.
- cosx = 1/2 is not a solution because it is in quadrants 1 and 4. So we move onto the next value which is x=π. This value works because it's greater than π/2 and smaller than 3π/2.
Okay, this is the last question of our pre-test. I was a bit confused when 1+cos2x changed to 1+2cos^2x-1 but you need to remember the identities because cos2x=2cos^2x-1. You also need to remember that sec^2x-1=tan^2.
When you repeatedly do the questions it's easier to remember all the identities...
* sorry if i didn't use colour or anything extra, i was using an older computer, at the time, and i was limited on tools. (: if i didn't anything wrong please comment & i'll correct it. The next scribe for wednesday is Bryan..
The pre-test contain eight questions..
1) Simplify: sin(2x+π)
A. sin2x
B. cos2x
C. -sin2x
D. -cos2x
The answer is C because sin(2x+π) is similar to sin(α+β) and the equation for this is simple, just do the sine dance!
sin(α+β)=sinαcosβ+cosαsinβ .. now you just plug sin(2x+π) into the equation
sin(2x+π)=sin2xcosπ+cos2xsinπ
sin(2x+π)=sin2x(-1)+cos2x(0)
sin(2x+π)=-sin2x+0
sin(2x+π)=-sin2x
cos π= -1
sinπ= 0 anything multiplied by 0 equals 0 so the right side reduces..
2) The terminal arm of an angle Ө in standard position passes through point (m,n) where m>0, n>0. Determine the value of sin(π+Ө).
A. ( -n)/√(m^2+n^2)
B. ( -m)/√(m^2+n^2)
C. ( n)/√(m^2+n^2)
D. ( m)/√(m^2+n^2)
The answer is A.
The question says that m and n are both positive so you know the coordinates are in the first quadrant.
m=x coordinates
n=y coordinates
Ө= angle
Once you draw a diagram you can use the pythagorean theorem to find the hypotunse, which is √(m^2+n^2).
Since sin=Opposite/adjacent then..
n/√(m^2+n^2)
BUT... it asks for the value of sin(π+Ө) so you substitute it in the sin(α+β)=sinαcosβ+cosαsinβ when you finish you get -sinӨ. Soo.. you multiply everything by -1.
And your answer is
-n/√(m^2+n^2).
Question# 3.
In this slide mr.k drew a diagram of cos A and you realize that the sin of this triangle is the sin of sin B... this means that both A and B are the same angle. The question is asking for the value of cos (A-B) and since A and B are the same the answer will be zero!
cos(A-B) = cos 0
= 1 < the answer is one because 1 is the raduis always 1 in the unit circle.
Question #4.
In this slide instead of having 2cos^2x+cosx-1=0 we let cosx=A so it's easier to read...
after we factored it to find the values of A.
- cosx = 1/2 is not a solution because it is in quadrants 1 and 4. So we move onto the next value which is x=π. This value works because it's greater than π/2 and smaller than 3π/2.
Okay, this is the last question of our pre-test. I was a bit confused when 1+cos2x changed to 1+2cos^2x-1 but you need to remember the identities because cos2x=2cos^2x-1. You also need to remember that sec^2x-1=tan^2.
When you repeatedly do the questions it's easier to remember all the identities...
* sorry if i didn't use colour or anything extra, i was using an older computer, at the time, and i was limited on tools. (: if i didn't anything wrong please comment & i'll correct it. The next scribe for wednesday is Bryan..
Monday, October 29, 2007
Sunday, October 28, 2007
POOF Can You weiveR These Please?? I got crust in my eyes...
I thought I saw snow outside of Sargent Park the other day. I clearly don't trust my eyes either. Is it just me or is the 
on slide 11 (of Friday's slides) really suppose to be positive? (-20) - (-36) = +16?? I could be goin' crazy tho cuz Mr. K is rarely wrong...
on slide 11 (of Friday's slides) really suppose to be positive? (-20) - (-36) = +16?? I could be goin' crazy tho cuz Mr. K is rarely wrong...Friday, October 26, 2007
Thursday, October 25, 2007
Identities
Whats up everyone! Im scribe for todays class. ALANNA!
I know its a crappy picture but you can see it in todays slides none the less you should be able to recognize it.
1. Given sinA= 4/5 cosB=-5/13. With cosA<0>0. Find cos(A + B)
-The best start off for this question is to draw a diagram which we have done, just so it makes it easier to determine the equation that we will be using later on.
-Now, since we are trying to find cos(A + B) we will write the rest of the equation that goes along with it.
Recall:
Its the sine dance! The equation that goes along with cos(A +B) is written as: cos(A + B)= cosAcosB - sinAsinB
-Then we plug in the specified #'s from the diagrams we drew. So cosA is (-3/5) because in the alpha diagram the cosA is adjacent over hypotenuse. just keep plugging in the numbers for the rest of the equation.
-Once your done writing out the rest of the equation work them out by getting the common denominator. You should end up with the answer -33/65. Which results with the answer being in Quad. III.
Now its nearing the end of class and he quickly introduced Proofs of the Sum and Difference Identities.
If we rotate diagram 1 so that R equals 90 degress and P is on the axis it will look like diagram 2. pretty much everything shifts clockwise.
Q'P' = QP
Now what we have to do is find the distance from Q'P' by using the distance formula:
= √((cos A- B) - 1)² + ((sin A - B) - 0)²
= √(cosA - cosB)² + (sinA - sinB)²
Around here Mr.K was totally rushing everything haha. Trying to finish the question before the bell rang. I didn't really understand a word he said after this plus I could no longer see the smart board cuz he was so busy writing.
Besides the end of the class it was pretty ok math that we learned today. Very understandable. Hope you got something out of my blog.
Drum roll please. "Attention! The next scribe is..........Derek!" ( I picked it randomly!)
Well todays class, in my opinion went very quick yet it was compact because we were introduced a new topic in math today called Proofs of the Sum and Difference Identities.
First we started off the class with the usual identities problems. Nothing new there because it was all straight forward unless if you havent been doing your homework.
OK now onto math!
I know its a crappy picture but you can see it in todays slides none the less you should be able to recognize it.
1. Given sinA= 4/5 cosB=-5/13. With cosA<0>0. Find cos(A + B)
-The best start off for this question is to draw a diagram which we have done, just so it makes it easier to determine the equation that we will be using later on.
-Now, since we are trying to find cos(A + B) we will write the rest of the equation that goes along with it.
Recall:
Its the sine dance! The equation that goes along with cos(A +B) is written as: cos(A + B)= cosAcosB - sinAsinB
-Then we plug in the specified #'s from the diagrams we drew. So cosA is (-3/5) because in the alpha diagram the cosA is adjacent over hypotenuse. just keep plugging in the numbers for the rest of the equation.
-Once your done writing out the rest of the equation work them out by getting the common denominator. You should end up with the answer -33/65. Which results with the answer being in Quad. III.
Now its nearing the end of class and he quickly introduced Proofs of the Sum and Difference Identities.
If we rotate diagram 1 so that R equals 90 degress and P is on the axis it will look like diagram 2. pretty much everything shifts clockwise.
Q'P' = QP
Now what we have to do is find the distance from Q'P' by using the distance formula:
= √((cos A- B) - 1)² + ((sin A - B) - 0)²
= √(cosA - cosB)² + (sinA - sinB)²
Around here Mr.K was totally rushing everything haha. Trying to finish the question before the bell rang. I didn't really understand a word he said after this plus I could no longer see the smart board cuz he was so busy writing.
Besides the end of the class it was pretty ok math that we learned today. Very understandable. Hope you got something out of my blog.
Drum roll please. "Attention! The next scribe is..........Derek!" ( I picked it randomly!)
Wednesday, October 24, 2007
Scribe Post, Monday Oct. 22 (Late) Alvin G.
Hey guys its Alvin. Sorry for the really late blog. Ill try to post what happened in class that day and hopefully be able to help you.
The first thing we learned was sin^2X + cos^2X = 1 (X = Theta).
This is also similar to the Pythagorean Theorem.
a^2 + b^2 = c^2
a = sin
b = cos
c = 1
This equation states that sin^2X + cos^2X can also be called 1. It also works the other way around; as for 1 can also be interpreted as sin^2X + cos^2X.
*From pc40sf07 slide oct. 22, 07.
The corollaries are like the sin^2X + cos^2X = 1 meaning that the left equations are equal to theyre right side. as for the right equations equal the left side.
In conclusion, this is about everything i remember from monday. Except from the group work that we did, if you are interested though it is on our oct. 22, 2007 slide. With this problem of mine, i believe that our study group would prove as a great asset. i just hope that I make sense of most of it before we go any more farther.
*I like the sine dance =) btw.
Scribe Post: Trigometric Identities & the Sine Dance!
Hello, hello! This time I'm going to get straight to the point... after this RIDDLE!! XD
I actually downloaded the SmartBoard Software and made a slide ^___^ but it turned out to be pretty small. It's better if you put it in full view.
I didn't explain all of the problems discussed in class because I don't believe that I have too. The best way of understanding this unit, I think, is by actually doing it. So have fun and DO YOUR HOMEWORK! (Which I believe is Exercise 14)
So sorry that I always post late!
Horray finally done! Now I don't have to worry for at least 2 months? Hopefully..
Next scribe is dun dun dunnnnnn
ALANANANABANANANANANANA
You can ask me tomorrow for the answer... agian."What is it that you cannot hold even ten minutes, even though it is lighter
than a feather."
I actually downloaded the SmartBoard Software and made a slide ^___^ but it turned out to be pretty small. It's better if you put it in full view.
I didn't explain all of the problems discussed in class because I don't believe that I have too. The best way of understanding this unit, I think, is by actually doing it. So have fun and DO YOUR HOMEWORK! (Which I believe is Exercise 14)
So sorry that I always post late!
Horray finally done! Now I don't have to worry for at least 2 months? Hopefully..
Next scribe is dun dun dunnnnnn
ALANANANABANANANANANANA
Tuesday, October 23, 2007
Scribe Post: Trigometric Identities
Hello everyone! This is LiON! I’m finally the scribe!! I've been dreading for this day. Horray, I'm last. I kinda feel forgotten. OH WELL
Anyways, I wanted to start off with the riddle I gave everyone.
“When you have it, you want to share it. Once you share it, you don't have it.”
No cheating! Let's see if you can get it and ask me tomorrow.
Okay moving on to math...
Today Mr. K gave us a surprise quiz. Well, I thought it was a surprise! I didn't expect it at all! I'm sure no one expected it too.
I’m not really articulate or good at explaining with words. It’s easier for me to describe something with pictures so I’m sorry if I don’t help make things clear but I’ll try my best!
Remember Mathematics is the science of patterns!It’d be easier if you could remember all the different things that equal to each other for this unit.
I’m really not good at this. I have no idea if there’s a simpler way of explaining this than what’s on the slide already. Hmm…
Anyways, I wanted to start off with the riddle I gave everyone.
“When you have it, you want to share it. Once you share it, you don't have it.”
No cheating! Let's see if you can get it and ask me tomorrow.
Okay moving on to math...
Today Mr. K gave us a surprise quiz. Well, I thought it was a surprise! I didn't expect it at all! I'm sure no one expected it too.
I’m not really articulate or good at explaining with words. It’s easier for me to describe something with pictures so I’m sorry if I don’t help make things clear but I’ll try my best!
Remember Mathematics is the science of patterns!It’d be easier if you could remember all the different things that equal to each other for this unit.
I’m really not good at this. I have no idea if there’s a simpler way of explaining this than what’s on the slide already. Hmm…
So the first thing we have to do is change sec Θ and tan Θ to sine and cosine which becomes(WHY CAN'T I UNDERLINE T_T)
Thus proving a) as the correct answer.
1st we have to change cos² Θ to sine. Because
Since we know that: tan² Θ + 1 = sec² Θ
Then you can manipulate it 1 - sec² Θ = - tan² Θ
Tah daH!
After we finished correcting the quiz we went into groups and started doing more complicated problems.
I really don't know how to explain the rest of the slides T_T I think it’s pretty self explanatory…
The Q.E.D. is an abbreviation of the Latin phrase "quod erat demonstrandum" (literally, "which was to be demonstrated", and figuratively, "I rest my case").
- Wikipedia
It’s basically saying that you have proven that it’s equal. In other words like saying, “HA! MY ANSWERS RIGHT!”
I feel like this scribe post was useless and ugly T_T …
Well, next scribe is ME! X)
Monday, October 22, 2007
Friday, October 19, 2007
Scribe Post: Trigonometric Idenities
Hey sorry for the late bloging but i never had a chance to check the blog to see whos the next scribe and when i came on there was a lot of BOB posts but of course i should of thought to have search by labels
now remembering back to yesterday Oct 18, we had two classes.
The First class we did a "pre-test" to prepare us for today's test hope everyone did well.
so now on with the new stuff well sort of...
Trigonometric Idenities:
In this unit the two important functions are sin(x) and cos(x) as we most of us may know already or will find out
using fundamental identities we can Simplfy a question
now remembering back to yesterday Oct 18, we had two classes.
The First class we did a "pre-test" to prepare us for today's test hope everyone did well.
so now on with the new stuff well sort of...
Trigonometric Idenities:
In this unit the two important functions are sin(x) and cos(x) as we most of us may know already or will find out
using fundamental identities we can Simplfy a question
So the following problem:
sin(x)sec(x)cot(x)
we know from the above image that sec(x) and cot(x) become 1/cos(x) and cos/sin(x)
now there will be a sin(x)cos(x) on both top and bottom of the fraction which will cancel out each other leaving 1.
and basicly thats about what we learned, as for next time i will try to be a little more careful and get this done much sooner sorry for the late scribe once again
looking at the list there some names that haven't been crossed out yet soooo next scribe is Alvin?
BOB
Those darned questions with the dates, if I see one anytime soon, i bet anything I'll freeze up. My moment of clarity was probably when Mr.K reviewed the BOB's and showed us how the reciprocal graph worked (fourth time showing me). Creating equations was quite complicated back then, but eventually I got used to it, just a but though. I think everything else is down pact, I can't wish you all good luck for I'll need it.
Thursday, October 18, 2007
B.O.B
Hmm... My muddiest point I'd have to say is drawing the inverse. Hard to explain but I'll try. I can't tell the difference from drawing the "mirror" effect inverse, to the kind of inverse that uses asymtotes etc. I think that's pretty much the only thing I have trouble on. Like I don't know which one to use. I'm prolly confusing right now. It used to be the word problems but I pretty much have it down now so thats good. Everything else in math right now is really straight forward to me except drawing the inverse.
BOB
Most of the things are clear to me, but after reading a few of the BOB's I also do have problems like Ivanna. Not so much as the reciprocal graphs but more on the word problems. I just get so mixed up sometimes, with the words and I tend to miss some key words that eventually cost me half a mark, a whole mark, or the whole she-bang(William Hung ftw!). Moreover, I also have problems remembering the equations, not so much that I can't figure it out, but more towards actually consuming too much time into that question that it eats off like 5-8mins of a stairdown. I'll try to fix it by doing a few questions tonight before bed. Goodluck on your tests everybody!
-Alvin G.
-Alvin G.
B.O.B.
My muddiest point, i would say is most definitely the word problems. it has always been my muddiest point because i just cant seem to understand what the question is asking or telling me. i can't blame my self? English is a second language to me! hahah... but anyways, i like how our class is doing, when we do a quiz or anything else and we get into our group of 3's or 4's and we figure out the questions on our own... its very helpful and we learn alot and we learn from our mistakes.
This is my second time taking pre cal 40s and i don't regret a thing. i didn't take two of the same courses with the same teacher nor at the same school. last year i took pre cal 40s at maples collegiate and i thought it was quite easy only if you did your homework every day. but once i returned back to Daniel McIntyre, i knew it would be challenging taking the course with Mr k. since i did once had him for my pre cal 20s. it's very different though i must say. the things we've just learned such as the word problems, I've actually never learned that, or maybe none that i know of and its very confusing but I've looked through the scribes and notes etc, and I'm quite sure i understand most of it. anyways, you'll hear more from me on the day before the next test.
Mr. K's pre cal 40s fall'07 class is a bunch of smart intelligent rabbits and i believe that every single one of my class mates will do terrific. just click on your heels three times and BAM!@#*! you'll do great! break a leg
This is my second time taking pre cal 40s and i don't regret a thing. i didn't take two of the same courses with the same teacher nor at the same school. last year i took pre cal 40s at maples collegiate and i thought it was quite easy only if you did your homework every day. but once i returned back to Daniel McIntyre, i knew it would be challenging taking the course with Mr k. since i did once had him for my pre cal 20s. it's very different though i must say. the things we've just learned such as the word problems, I've actually never learned that, or maybe none that i know of and its very confusing but I've looked through the scribes and notes etc, and I'm quite sure i understand most of it. anyways, you'll hear more from me on the day before the next test.
Mr. K's pre cal 40s fall'07 class is a bunch of smart intelligent rabbits and i believe that every single one of my class mates will do terrific. just click on your heels three times and BAM!@#*! you'll do great! break a leg
B.O.B.
My absolute muddiest point in this unit were the reciprocal graphs and word problems. The concepts and solutions for the both of them don't make much sense to me. I also have a lot of trouble in remembering how to write equations for graphs. The easiest part in the unit was graphing the "absolute graphs". I hope I pass the test tomrorow, good luck to everybody.
Cheers,
Ivanna
Cheers,
Ivanna
BOB
I found the most difficult thing in this unit was inverse and reciprocal of functions. I was confused with these functions. It's hard to remember the difference between these two.
I also have trouble to graph for words problems. The hardest thing for word problem was how to get the period. I guess I understood how to get the period after Mr. K explained today's test.
I went over some of the examples, hoping that I do remember and do good on the test.
Good luck to everyone tomorrow! :)
I also have trouble to graph for words problems. The hardest thing for word problem was how to get the period. I guess I understood how to get the period after Mr. K explained today's test.
I went over some of the examples, hoping that I do remember and do good on the test.
Good luck to everyone tomorrow! :)
BOB
Honestly, it's hard for me to create an equation, for example create a cosine equation, create a sine equation because I don't know what the exact number should be use to get the correct answer. I get confused easly, but I know how to place them and to identify them. Another thing that bothers me is graphing. I know what to do but when the time comes that you have to graph it, I get totally lost!BOOM! Good thing i love to draw.. anyways....Transformation and inverse function is tricky.. but I found the lesson interesting and that keeps me on going.
This is rosselle by the way.. I used Jordan's account because i forgot mine...
This is rosselle by the way.. I used Jordan's account because i forgot mine...
Blogging On Blogging
For this unit on transformations i didn't really have much trouble in, however i was confused about inverse and reciprocals but i figured it out.
One of my biggest mistakes and would cause me to lose a lot of marks is i don't fully understand or read a questions properly, mostly because i feel rushed to finish things within a time limit. So i will try to focus more on what the question is saying and write down important information before continuing on.
I believe i covered everything, now all i have to accomplish is to study more and use my spare time more efficiently
One of my biggest mistakes and would cause me to lose a lot of marks is i don't fully understand or read a questions properly, mostly because i feel rushed to finish things within a time limit. So i will try to focus more on what the question is saying and write down important information before continuing on.
I believe i covered everything, now all i have to accomplish is to study more and use my spare time more efficiently
BOB 'in
Hey its Anthony again. This is my bob.
The things i find most difficult about transformations is remembering the difference between f inverse and reciprocal. Also i have trouble remembering how to solve each of the transformations. In example today's pre test. when we were asked to write an equation for the inverse if the original equation. I understood that all the Y's be came X's and vice versa, except i forgot the steps on how to do it. I am also worried about the amount of stress tests put on me mentally. I just find it so nerve racking and i over analyse questions. I tend to panic. Some smaller things i have problems with is inverse. Such as labeling a scale.
Good luck to everyone tomorrow. I better go study
The things i find most difficult about transformations is remembering the difference between f inverse and reciprocal. Also i have trouble remembering how to solve each of the transformations. In example today's pre test. when we were asked to write an equation for the inverse if the original equation. I understood that all the Y's be came X's and vice versa, except i forgot the steps on how to do it. I am also worried about the amount of stress tests put on me mentally. I just find it so nerve racking and i over analyse questions. I tend to panic. Some smaller things i have problems with is inverse. Such as labeling a scale.
Good luck to everyone tomorrow. I better go study
Hi there. What I found difficult about this unit was the inverse and reciprocals of functions.
I got it mixed it up with eachother sometimes. But now since we went over it numerous times in class I finally got it. The other thing that also bothered me in this unit, was how to get the period of the function for the graph and how to find the equation. It got easier when we had to do those work sheets then go over it in class within the groups we were put in. Overall, I think this unit was alright. I'm just hoping I do good on the test tomorrow =/
-roslyn
I got it mixed it up with eachother sometimes. But now since we went over it numerous times in class I finally got it. The other thing that also bothered me in this unit, was how to get the period of the function for the graph and how to find the equation. It got easier when we had to do those work sheets then go over it in class within the groups we were put in. Overall, I think this unit was alright. I'm just hoping I do good on the test tomorrow =/
-roslyn
BOB
Hm. Well, for this unit, I found it a bit complicated. Sometimes i would get confused with the inverse and the reciprocal, i'm crazy that way. But when we did the quiz yesterday, I was really glad that we corrected it together because it finally clicked for me. Solving the problems was sometimes a bit difficult for me only because I get all jumbled up with the information given. But when we do the problem together, I really got some clarity because I see how it is broken down. By doing the problems together, I'm able to point out the mistakes that I made by solving it alone and trying not to do that same mistake in the next problem. I'm really comfortable solving problems now; I just have to watch for little mistakes that I could make (such as forgetting to scale my graphs ... -_-; ). I think I'll do okay tomorrow ... can't get too confident or i might fail haha. Well, that's pretty much all I can say about Transformations. Good luck to everyone on the test tomorrow =) !
Blogging on blogging
I haven't had a lot of problems with this unit, just little adjustments I have to make on my own in order to get full marks on my test. For example up until today's classes I was unprepared in solving for the outputs for more complex sine and cosine functions. My moment of clarity was again today going over the problems that I was having normally. The hardest part was the even and odd function but again now I understand what to do when having that kinda problem put in front of me.
BOB
Okay. Well, i found this unit to be a bit confusing for me. Like what most of the people have said, I too have had difficulty with the inverse and reciprocal. On the last quiz we took I went completely blank and mixed up everything. But, going over these questions have helped me understand it a little bit more. I find it interestng how I understand it so well when we're working on questions either together in groups or together as a class. Or how I'd undestand it when I'm doing my work, and then screw up on my quizes. Other than the confusion with the inverse and reciprocal, I'm pretty okay with the other stuff. Hopefully, I'll do good on the test. Goodluck to everyone :]
BOB
I'm happy to say that I've made some changes for the better during this unit. In the beginning I was lost and the things that Mr. K was teaching wasn't sticking to my mind. After a couple of visits with Mr. K during lunch hour, I was able to really understand the concept of this unit. Working together with my classmates in our groups was also very helpful since they would sometimes have the same questions as me. I also felt more comfortable asking them questions and working together on problems and talking with them made learning better. I hope everyone does a great job on tomorrow's test !
Blogging on Blogging
Okay..In this unit, I'm a little confuse of graphing f^-1 (x) and 1/f(x). I always do it the other way. Sometimes, i reflect my graph using y=x instead of finding the reciprocal graph. I'm also having a hard time with the problem solving questions but as Mr. K gave us time and let us practice with these questions, I'm getting used to solving it. Well, I think that's it. I'm okay with stretches and compressions of the graph, even and odd functions. I guess I'll do well in the exam if I keep practicing solving the inverses and reciprocal questions.
BOB
hey, okay here's is my blogging on blogging. For this unit i didn't have that much problems with understanding the concepts. For the first couple classes i didn't understand the inverse graphs or what was an even graph and what was an odd graph. I found out, by asking classmates, that the inverse of a function is just a reflection over x=y. So you simply let the y coordinates equal the x coordinate and vice versa. When it's odd you just turn it 180 degrees around and that's how it's suppose to look like. But for even functions i rememebered that you let the the x coordinates become negative when you check if it's even. But i'm not certain how you graph it, do you just let the x coordinates become negative and then graph it with the new x and y coordinates? Besides this, i haven't been able to recall any major problems I had during this unit. I always forget to label my scale on quizzes. Oh wait, when you say a function is symmetric does that mean it's like cosine and you can draw a line through the middle and it's the exact same on each side? I remember exercise nine had a couple questions relating to this.. I also had a bit of trouble with the concept of graphing absolute value functions. My moment of clarity has arised but not to it's full potential because i remember on a quiz i blanked and forgot it all. Now I'm worried if i don't understand it fully. I know how to graph the line but when it comes to the second part where you must draw the absolute value i'm lack confidence and i'm unsure. I know that it must equal positive when there are straight brackets around the variable but do you just forget about the negative part on the graph? If that makes any sense I need some help. Other than these few concerns I can't remember any others..
B.O.B.
Well first of all I can say that this is one part of the lectures that I am having trouble with. But as time goes on I understand little by little all the topics. Even though I am having trouble with some questions. At first I don’t understand if there is a number before the “x” for example: (1/2)x the graph will going to stretched even though it is a small number and the graph will going compress if the variable before the “x” is big for example: 2x.
Well at least now I know. And also at first I am having about the inverse function but because of our pre-test this early morning I barely understand now what is inverse function. Well I guess we really have to study hard to pass our exam tomorrow.
Good luck to us!!!!
BOB
For the most part, I pretty much understand what we were doing in this unit, although I sometimes make stupid mistakes when it comes to tests and quizzes on the little things. To fix that I guess I would have to pay more attention to detail and make sure that I read the questions carefully. Now in regards to this unit specifically, I would have to say that one of the hardest things is trying to remember how to draw all the graphs and trying to remember all the steps and rules that apply to them, because there are quite a few different ones. Moving on, I guess I can say that I had a "moment" when we were learning how to draw reciprocal graphs, because at first I was confused about how to determine whether the lines where approaching zero or infinity, because I wasn't very clear on the whole biggering and smallering concept, but then we started doing examples and Mr. K was explaining it more and it somehow just clicked. So that was a good thing because now I know how to draw it properly. Something that I probably need more practice on is the words problems, because they can sometimes be really tricky and the thing about them is that you have to be really accurate with your work because if you have the wrong graph, you'll have the wrong equations and if your equations are wrong, you'll get the wrong answer and that would really suck. As for everything else, I think I understand it fairly well, but I still need to do some reviewing to make sure. Okay, well good luck guys (:
Blogging on Blogging for Transformations
Well for this unit I didn't really have much trouble with it. I would have to say my "moment of clarity" would have to be when we were starting out the reciprocal graphs. I didn't really understand before how the values that were small would suddenly get bigger until I realized that the values under one were fractions. So when you go the reciprocals of those numbers they would all be bigger than one, and vice-versa for the original values bigger than one. Probably the most difficult thing I found in this unit was making the inverse graph over y = x. Even though I know how to make inverse graphs I don't really know how with the y = x method. I sometimes have problems making the graphs in the Trigonometric Modeling questions, even though I find it really fun to do. The parts that I liked most about this unit is the Trigonometric Modeling and the Reciprocal Graphs.
BOB
This unit is quite difficult and sometimes confusing for me, but after Mr. K had given us some examples and explained the proper way to do it...i've been able to understand everything so far.
The other day, when we had our short quiz about graphing reciprocals I was kinda lost, and wasn't paying attention to the directions and cost me to loose marks. But after we corrected it I totally understand it now...i found out that this unit was way easier than the last unit.
Anyways, Goodluck to everyone!
The other day, when we had our short quiz about graphing reciprocals I was kinda lost, and wasn't paying attention to the directions and cost me to loose marks. But after we corrected it I totally understand it now...i found out that this unit was way easier than the last unit.
Anyways, Goodluck to everyone!
BOB
So far, I understand most of it fairly well. I kinda thik that this unit is easier to understand than th elast one, the unit circle ones. This has little things to memories and I just got confused on few things. I am more comfortable with this unit since Mr. K. gave us lots of review which really helped for me in remembering what our lessons were. My mistakes usally come from either not reading or understanding the quetions well or I forgetting the steps to do. Like which one should we do forst or find first, but good thing Mr. K. always have this little ways to memorize things. Like the DABC thing, i could easily make an equation from a graph. And uhm i sometimes get mixed up with the reciprocal function and the inverse but since Mr. K. teaches us the baby clean up thing I just need to remember that thing and everything started to be ok. Overall, I understood almost everything fairly well, good thing Mr. K. gave us plenty of review questions which really helped a lot!!!
GOOD LUCK EVERYBODY!!! ;P
GOOD LUCK EVERYBODY!!! ;P
Bob
I'd like to take this opportunity, since I haven't been scribe yet, to say that I really like the way Mr.K teaches. How he puts a problem on the board and waits for volunteers to go up and if another student thinks it's incorrect to go up and correct it. I love how a lot of us also discuss what we think is wrong.
Okay, now to start with Bob.
I've been able to understand everything we've done so far like the word problems and the transitions, except for graphing reciprocals. I understand where to put the asymtotes, I just don't know where to put the points and everything else from there.
I also have a problem paying attention to detail. I always make small mistakes on tests and quizzes that cost me to loose a lot of marks. It's just something I have to work on.
ganbatte minasan!
(Good luck everyone!)
- L i O N
Okay, now to start with Bob.
I've been able to understand everything we've done so far like the word problems and the transitions, except for graphing reciprocals. I understand where to put the asymtotes, I just don't know where to put the points and everything else from there.
I also have a problem paying attention to detail. I always make small mistakes on tests and quizzes that cost me to loose a lot of marks. It's just something I have to work on.
ganbatte minasan!
(Good luck everyone!)
- L i O N
BOB
Here's my BOB!
I think I understand most of the part in this unit, Transformations.
The only thing that irritates me is when we are writing quizzes and tests,
I always make silly mistakes that i need to avoid. For example, I don't
read the questions carefully.
The grouping in class is fun. It makes us know other people in the class,
and learn the lesson better.
Aim to Ace the test! :D
Good luck to everyone!
I think I understand most of the part in this unit, Transformations.
The only thing that irritates me is when we are writing quizzes and tests,
I always make silly mistakes that i need to avoid. For example, I don't
read the questions carefully.
The grouping in class is fun. It makes us know other people in the class,
and learn the lesson better.
Aim to Ace the test! :D
Good luck to everyone!
Wednesday, October 17, 2007
Bob-ing
Well I guess I'll begin with my muddiest point(s). I really don’t like word problems. Period. It just throws me off somehow. I know how to do most of the work in this unit, just throw in some more words in the question and I suddenly don’t know what to do. Well that’s not the only thing that bothered me.
The type of word problem we did repeatedly in class with essentially the same questions gave me some constant trouble. Particularly where it asks “For how long…” or “At what time…” You know, the ones where it gives us the Y cord and we need to find the X cord(s). Yeah I don’t know how to completely.
Next I will explain that “moment of clarity” for me. It came with Reciprocal graphs. While I was doing my scribe for it I got some help and “poof”. It was explained to me as to how it worked. After I figured out how they worked I was really happy, because I could finish my scribe post!
On a side note…
Completely forgot how to do the calendar graphs until I seen it today on the review. Particularly the scaling. I know there’s some number system we did for the scale, and we were suppose to start at December something the year before. I don’t know…
Completely forgot about inverse functions until yesterday. Don’t know anything about them much…Switch the x and y cords? Isn't that the reflection in the y=x line? So is an inverse function just that? I don't know...
Having trouble remembering the different Stretches and what not.
One last questoin: How do you do a stretch on a line?
Aside from all that stuff above I think that I'm doing well with the other concepts.
Scribe Post
Greetings.
This present day we got straight to the point, and we began our second quiz on Transformations! woo.
20 minutes go by...
Sweat dripping on papers, palm's moist, and mouth's dry from the intensifying surge of power radiating from our quiz sheets. "Time's up! Time's up! Time's up!" yells Mr. Kuropatwa. Thirty sweat, and acne filled faces look up at the clapping hands of Mr. K as he commands us to advance our papers to the front of the classroom.
And so the alteration of our papers begin:
Odd Function: Symmetric with respect to the origin
Average-Minded Definition of an Odd Function: If you rotate the graph of the function 180 degrees: it'll be the same
We are told that this function is an Odd Function, ergo we must complete it.
This is the completed graph. woo.
Now let's put it to the test!...
Would you look at that! I have rotated the graph 180 degrees, and it looks completely identical!
Next question...
Graph the Reciprocal of the function.
Facts we know:
Dotted Blue Line: Vertical asymptote, where y= 0
Yellow Points: In-variant points, where y= 1, and y= -1
Green Line: Reciprocal of the horizontal line coordinates (x= 2 - 4 , y= 3)
Next Question...
Next we are asked to sketch the graph of f(x) = 1 /| x-2|
To answer this question, we must first find the graph of f(x) = |x+2|
BUT BEFORE we find the graph of f(x) = |x+2|, we MUST first find the graph of
f(x) = x-2
Red Dot: -2 is a y-coordinate of the line
Blue Dot: Slope of the line is (rise/run) in this case it's (1/1); moving up once from -2, and moving to the right once ending in coordinates (x= 1 , y = -1)
To turn it into |x-2| : all negative coordinates turn positive:
To find the reciprocal of the function we use the
Facts We Know:
Final Question...
With the function y= x , we are to expand it vertically by a factor of 2, shift it 3 units to the left, and take its reciprocal. With this new function we are asked to write a new equation for it, and sketch it on a graph.
First we'll write the Equation:
y = x
The first thing the question asks us to do is to expand the function vertically by a factor of 2. We accomplish that by writing
f(x) = 2x
Afterwards we must shift the function 3 units to the left, so the equation becomes:
f(x) = 2(x+3)
Finally we take it's reciprocal which is basically flipping it, switching the numerator, and the denominator's positions.
f(x) = 1/[2(x+3)]
or
f(x) = 1/(2x+6)
With this new equation; we can sketch the graph to this new function derived from y = x.
To sketch this function we must first sketch f(x) = 2x+6
6 - y-coordinate of function
2/1 - slope of function
Now we take the reciprocal of the function with our FACTS
And there you have it a sketch of the new function.
-----------------------------------------------------------
It's been fun, I love spending my Wednesday mornings (2am) working on math stuff. Anyways here's a joke I have been holding in every time Mr.K asks us if we had any good jokes.
woo! Here it is:
An anion was walking down the street, and he saw a cation. The cation was looking pretty sad, so the anion went up to him, and asked him if anything was wrong. The cation looked at him and told him he had lost an electron. The anion asked him, "Are you sure?" and the cation said, "I'm positive!"
*Thanks Jasmin for refreshing that for me*
Hopefully you all understood that, I'm hoping.
SO, onto the juicy part that everyone skips to, and misses everything i wrote to check if they're the scribe post for the next day... muahaha time to put a frown on someone's face.
My buddy!! JOE S!! Your next, put down your psp.
This present day we got straight to the point, and we began our second quiz on Transformations! woo.
20 minutes go by...
Sweat dripping on papers, palm's moist, and mouth's dry from the intensifying surge of power radiating from our quiz sheets. "Time's up! Time's up! Time's up!" yells Mr. Kuropatwa. Thirty sweat, and acne filled faces look up at the clapping hands of Mr. K as he commands us to advance our papers to the front of the classroom.
And so the alteration of our papers begin:
Odd Function: Symmetric with respect to the origin
Average-Minded Definition of an Odd Function: If you rotate the graph of the function 180 degrees: it'll be the same
We are told that this function is an Odd Function, ergo we must complete it.
This is the completed graph. woo.
Now let's put it to the test!...
Would you look at that! I have rotated the graph 180 degrees, and it looks completely identical!
Next question...
Graph the Reciprocal of the function.
Facts we know:
- Vertical Asymptote is where y= 0 because the reciprocal of the point is undefined
- The In-variant (unchanging) points are where y= 1, and where y= -1
- Class is long
Dotted Blue Line: Vertical asymptote, where y= 0
Yellow Points: In-variant points, where y= 1, and y= -1
Green Line: Reciprocal of the horizontal line coordinates (x= 2 - 4 , y= 3)
Next Question...
Next we are asked to sketch the graph of f(x) = 1 /| x-2|
To answer this question, we must first find the graph of f(x) = |x+2|
BUT BEFORE we find the graph of f(x) = |x+2|, we MUST first find the graph of
f(x) = x-2
Red Dot: -2 is a y-coordinate of the line
Blue Dot: Slope of the line is (rise/run) in this case it's (1/1); moving up once from -2, and moving to the right once ending in coordinates (x= 1 , y = -1)
To turn it into |x-2| : all negative coordinates turn positive:
To find the reciprocal of the function we use the
Facts We Know:
- Vertical Asymptote is where y= 0 because the reciprocal of the point is undefined
- The In-variant (unchanging) points are where y= 1, and where y= -1
- And yes class is long
Final Question...
With the function y= x , we are to expand it vertically by a factor of 2, shift it 3 units to the left, and take its reciprocal. With this new function we are asked to write a new equation for it, and sketch it on a graph.
First we'll write the Equation:
y = x
The first thing the question asks us to do is to expand the function vertically by a factor of 2. We accomplish that by writing
f(x) = 2x
Afterwards we must shift the function 3 units to the left, so the equation becomes:
f(x) = 2(x+3)
Finally we take it's reciprocal which is basically flipping it, switching the numerator, and the denominator's positions.
f(x) = 1/[2(x+3)]
or
f(x) = 1/(2x+6)
With this new equation; we can sketch the graph to this new function derived from y = x.
To sketch this function we must first sketch f(x) = 2x+6
6 - y-coordinate of function
2/1 - slope of function
Now we take the reciprocal of the function with our FACTS
- Vertical Asymptote is where y= 0 because the reciprocal of the point is undefined
- The In-variant (unchanging) points are where y= 1, and where y= -1
And there you have it a sketch of the new function.
-----------------------------------------------------------
It's been fun, I love spending my Wednesday mornings (2am) working on math stuff. Anyways here's a joke I have been holding in every time Mr.K asks us if we had any good jokes.
woo! Here it is:
An anion was walking down the street, and he saw a cation. The cation was looking pretty sad, so the anion went up to him, and asked him if anything was wrong. The cation looked at him and told him he had lost an electron. The anion asked him, "Are you sure?" and the cation said, "I'm positive!"
*Thanks Jasmin for refreshing that for me*
Hopefully you all understood that, I'm hoping.
SO, onto the juicy part that everyone skips to, and misses everything i wrote to check if they're the scribe post for the next day... muahaha time to put a frown on someone's face.
My buddy!! JOE S!! Your next, put down your psp.
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