Reflection #5

okay, this week was pretty much easy. I caught on quickly to everything that we learned. We started on Chapter 5. It all had to do with exponents. There are seven rules you have to follow when solving for an exponent.

1) b^x . b^y = b^x+y
2) b^x/b^y = b^x-y
3) (ab)^x = a^x b^x
4) (a/b)^x = a^x/b^x
5) (b^x)^y = b^xy
6) b^x/y = y square root b^x
7) to solve:
a) write as the same base
b) set exponents =
c) solve for x

_______________________________________________________
Example:

1) (b ^2/a)^-2 (a^2/b)^-3

Distribute the exponent on the outside of the ( )
b^-4/a^-2 . a^-6/b^-3
If you have a negative exponent, then get rid of it. Put a one on top of the number and cancel the negative.
1/b^4 / 1/a^2 . 1/a^6 / 1/b^3
Cross out by cross dividing.

1/ba^4
________________________________________________________

Sometimes, some of the problems confuse me, but i am sure if i study that i will do good on the test. I just need more practice. So i will just do my homework every night, until i know what i am doing.

________________________________________________________

Friday we worked on logs. Logs are my favorite because they are so easy. And if you get confused while you are doing them, just get base ten and solve it in your calculator.

Example:

log base 2 of 16
log base 2 of 16 = x
2^x = 16 ( you have to make both of your bases the same, so....)
2^x = 2^4 ( make your exponents =)

x=4 therefore: log base 2 of 16 = 4

_______________________________________________________

I didn't really have trouble with the things that we learned this week, but i could use some more practice on exponents and logs. Oh, I didn't get the part where you had to make a sandwich and stuff, so if someone can show me a problem like that, that would be nice.. THANKS

Reflection 5

This week really wasn't bad. I'm getting better at math..I think, ha. But the thing I understood most is Logs. I never understood it until mrs robinson taught it to us this simple way.

logb^x=a
all you would do is switch the x and the a. (Kinda like an inverse)
b^a=x <---This is exponential form.

log3^2=7
3^7=2

This helps you solve problems sometimes.
But before you solve you have to change it to exponential form.

Example:
logx^4=2
x^2=4
x= +/- 2

For natural logs-
e^x=75
change e to ln(natural log), then switch the x and the 75
ln75=x
Plug into your calculator.
ln 75=4.317

------------------------------

For something I didn't get:
I don't understand how to do those sandwhich things.
They really confuse me. If someone would explain to me how to do it
that would be helpful.

Reflection #5

alright week five we learned how to use exponents, logs, and graph equations. the thing i understood the most was the logs. here's how you would work one:

log base b x=a
step 1:when putting this in exponential form you take the base set it rased to what the problem equals and set this equation equal to x.

b^a=x
step 2: this is exponential form the problem can no further be simplifyed.

***if given the equation log base 2 16, remember that if a equation is not set equal to anything set it equal to x.***

***if given the quation log 1020=x, remember that when there is not a base it is 10.***


heres an example:

log base 2 16=x
2^x=16
2^x=2^4
x=4
log base 2 16=4

heres some thing i didn't understand (b^2/a)^-2(a^2/b)^-3 i don't understand the sandwitch thing and i don't realy get how solve this problem. some help would be nice thanks..

Reflection 5

This week was ight it wasnt to bad sumtimes i still feel lost in something but other than that it was cool.
The i got most was what we went over today logs.
example...
log base 6 of 36
log base 6 of 36=x
6^x=36
so all you would have to do is switch the exponent and x to find the answer.
the you simplify and solve for x which would be 2

The reason why i could understand this was because it was very simple and easy and we just learned it today...

Reflection #5

Reflection 5

Well, wow! This week was both easy and difficult. We took the Chapter 4 test on Wednesday and i don't think i did bad on it (hopefully). We learned how to work multiple problems this week.

What i understood the most was the logs. I must say, it is super easy

EXAMPLE: Solving.
log base 2 of 16
log base 2 of 16 = x
2^x = 16
x = 4 => log base 2 of 16 = 4

EXAMPLE: 5^x = 125
x = 3 => log base 5 of 125 = 3

EXAMPLE: 10^x = 75
log base 10 of 75 = x
log 75 = x
log 75 ~ 1.875

EXAMPLE: e^x = 75
ln 75 = x
ln 75 ~ 4.317

That is what i seemed to understand the most this week. It is really simple and easy to work. But on the other hand i had some diffuculty with these types of problems from the notes we took on Wednesday:

EXAMPLE: (a/b)^x = a^x/b^x

Can anyone helpp?

Reflection #4- REDO!

OH WOW!
Being that i can finally get onto blogger successfully, i just realized how tiny my reflection was!

I'll redo it...



----------------------------------------------------------------------------------------------------------------------------------

This week was pretty intense and went by all too quickly, from FeFe and her "ALRIGHT, THAT IS ENOUGH!" to getting completely lost trying to relearn domain and range, this week was not my best.

On the bright side, functions were pretty simple to me so i should probably explain them:

First, let's start with the fact that if you find the function of x, or f(x), you will find y.

Adding or subtracting functions:
(f+g)(x)
f(x)+g(x)

(f-g)(x)
f(x)-g(x)

example:

f(x)=x+1
g(x)=x-4

(f+g)(x)= x+1+x-4
(f+g)(x)=2x-3

Multiplying functions:
(fxg)(x)
f(x) x g(x)

f(x)=2x+4
g(x)=4x-6

(2x+4)(4x-6)
F.O.I.L.= (8x^2-12x+16x-24)
=8x^2+4x-24

Finding a function of another function:
(fog)(x)=
f(g(x))

f(x)= 2x+4
g(x)= x-4

plug in the g(x) equation into the f(x) equation where ALL x's appear.

2(x-4)+4
distribute.
2x-8+4
(fog)(x)=2x-12
--------------------------------------------------------
Unfortunately, i'm still quite iffy on domain and range.
PLEASEEE, someone help me before the quiz tomorrow! :/

the semicircle is killing me.

thanksss!

so guys....


what did we have for homework?

Hey someone explain to me how to do the stuff we learned today.
I thought I understood it but when I went to do the homework, I couldn't do it.

Like for the ones where it's (#^-exponent)^-exponent
And the ones where it's (#^-exponent + #^-exponent)^-exponent

confusingggggggg.

Reflection #4

I understood how to find the domain and range of a square root:

1. Set the equation under square root sign = to zero.
EX: (square root of) x+5

x+5=0

solve for x

x = -5

then you would make a number line:

<--------(-5)-------->

Then you would plug in a number into the original equation. If your answer results in a negative then you would cross out that side of the number line. Once you find where you have a positive answer.

(-6) -ve

(-4) +ve

........[-5, infinite)

on the other hand, i do not understand the semi circle thing in our notes............

Refelction 4

O boy, where can i start. Well first let me just express my opninon on how i'm feeling right now. I am tired of typing and studing for test. I was out for a few days and i am still trying to catch up so i'm just in a P.O mood. I really aint in the mood for blogging or reviewing for anything else in math. I hope the quiz aint to hard. Lets just say ive been out of it all week and didnt pay any attention when i was in class. I'm lost just abouit on everything because i have never seen it before, but i know it would help so much more if i actually was reveiewing my notes and homework but o well i got whats coming for me if i fail. Hopefully i can get back on track monday. Anyways this week we went over a bunch of new stuff. The domain and rang stuff is easy to understand but you just got to review the notes to understand the steps. I like doin the fraction problem because all you got to do is set the bottom up for zero than u find all the points. If i can find anyime to reveiw that i will so i can pass my quiz but at this rate i'm going straight to bed.And now i just got yelled at for typing to loud cause my parents got to wake up early and they want to go to bed.hahaha I'm so lose with the f of x stuff and invereses right now that i couldnt even remember how to solve for y on one of the problems. Yes this has been my worst blog but i'm proud to say at least i did one. Night

Reflection #4.

This week was pretty intense and went by all too quickly, from FeFe and her "ALRIGHT, THAT IS ENOUGH!" to getting completely lost trying to relearn domain and range, this week was not my best.

On the bright side, functions were pretty simple to me so i should probably explain them:

First, let's start with the fact that if you find the function of x, or f(x), you will find y.

Adding or subtracting functions:
(f+g)(x)
f(x)+g(x)

(f-g)(x)
f(x)-g(x)

example:

f(x)=x+1
g(x)=x-4

(f+g)(x)= x+1+x-4
(f+g)(x)=2x-3

Multiplying functions:
(fxg)(x)
f(x) x g(x)

f(x)=2x+4
g(x)=4x-6

(2x+4)(4x-6)
F.O.I.L.= (8x^2-12x+16x-24)
=8x^2+4x-24

Finding a function of another function:
(fog)(x)=
f(g(x))

f(x)= 2x+4
g(x)= x-4

plug in the g(x) equation into the f(x) equation where ALL x's appear.

2(x-4)+4
distribute.
2x-8+4
(fog)(x)=2x-12
--------------------------------------------------------
Unfortunately, i'm still quite iffy on domain and range.
PLEASEEE, someone help me before the quiz tomorrow! :/

the semicircle is killing me.

thanksss!

Reflection 4

This week flew by because we had a four day week and Mrs. Robinson wasn't there for two of those days. We learned some more of domain and range, inverses, and axis of symmetry. I did not grasp all of the four concepts you use on domain and range, but my wonderful friend Matt helped me and now I get it so I hope I do good on the test tomorrow. Im going to show what the concept of domain and range I know how to do well and that is the absolute value one.

For absolute value the Domain is (-infinity, +infinity)

And Range is either (shift, +infinity) or (-infinity, shift) depending on the sign in front of the absolute value.

Example: -/x+2/+5

Then your domain would be (-infinity, +infinity) like always for absolute value.

And your range would be the negative one because of the sign : (-infinity, 5)


On the other hand I did not get how to find inverses at the end of the week.

Reflection 4

this week was alright, i really like only having 2 days, but i learned something in those two days. We learned about domain and range, inverses, and finding symmetry

y=x^2+2 find the symmetry

a. x axis
(-y)= x^2+2
y = x^2 - 2
reflection

b. y axis
y =(-x^2)+2
y = x^2 +2
symmetric

3. y = x
x = y^2 + 2
y^2 = x - 2
y = /x-2

4.(-y)=(-x)^2 + 2
-y = x^2 + 12
y = -x^2 - 2

this seems alright, but i still need some practice to get better and help me remember the steps. I dont like the inverse and sometimes i get stuck on some of those steps up there.

Reflection #4 (first one was a mess up)

This week was fairly simple because the only major thing we learned was domain and range.

So i'll expain how to find the domain and range of:

-a square root: 1. Set stuff under sq. root sign = to zero.
Sq. root of x+4.......so x+4=0......solve, you get x= -4.

now make a # line <_______-4_________>
plug a # on the left side of x-----^----and plug it in to the original eqn. If you get a # that is not real, cross out that side the number line. In this case, if you plug in -5 you get the sq. root of -1, which is i. so the # line on the left side of -4 gets crossed out. -3 gives you 1, so you keep that part of the number line. This means your answer is everything from -4 to infinity, so your answer in point form would be....dunt da na na.....(-4,infinity)

-an absolute value:
EASY! ok your answer will aways be either (-infinity, shift) or (shift,infinity) what that means is: /x-4/+2
-------------^----2 is your shift. now look in front the absolute value...no negative sign, so your answer goes in the (2,infinity) form because 2 is the shift.

now lets say the equation was -/x-4/+2 just as simple. Because there is a negative sign in front of the absolute value, your answer is in the other form...(-infinity,2)
_______________________________________________________________

Now the only thing I didnt understand this week was the whole semi circle thing......I have no clue how to do them. I hope they're not on the quiz tomorrow!!!!

Reflection #4

Reflection 4

Well, domain and range is very easy considering that some problems have a fixed domain. For example the Domain of every polynomial will be (-infinity, infinity). (-infinity, infinity) will also be the domain of every absolute value. The range of all polynomials will be (-infinity, infinity) if the polynomial has an odd degree. If the polynomial is a quadratic then its range will be [vertex, infinity) if the parabola opens up and (-infinity, vertex] if the parabola opens down. The range of all absolute values will be (shift, infinity) if the v opens up and (- infinity, shift) if the v opens down. To find the Domain of a fraction you: set the denominator equal to zero, Solve for x, Then set up your intervals like so (-infinity, lesser x), (lesser x, greater), (Greater x, infinity). Finding the range is unnecessary for us. To find the domain of a square root you: set the inside equal to zero, set up a number line, Test values on either side by plugging them in, Eliminate the negatives, then set up your intervals. Finding the range is unnecessary for us. Now the whole function thing is easy and hard for me at the same time. it is very hard to explain. I get adding, subtracting, multiplying, and dividing functions. But when it comes to finding an inverse things get a little hard for me. switching the x and y is easy, But proving it is hard for me. Well… I just sat here for 10 minutes and now I understand it, so nevermind.

reflection 4

this week went by pretty slow for me, even though we only had a 4 day week, but i learned more about domain and range, inverses, and finding symmetry

y=x^2+1 find any symmetry


1. x axis
(-y)= x^2+1
y = x^2 - 1
reflection

2. y axis
y =(-x^2)+1
y = x^2 +1
symmetric

3. y = x
x = y^2 + 1
y^2 = x - 1
y = /x-1

4.(-y)=(-x)^2 + 1
-y = x^2 + 1
y = -x^2 - 1

this concept seems easy to me, and i am currently having some trouble with plugging in correctly when working an inverse

reflection #4

this week we learned how to find symmetry...
for example: y=x^2+1
1. x-axis:
(-y)=x^2+1
y=-x^2-1; not symmetric

2. y-axis:
y=(-x)^2+1
y=x^2+1; symmetric

3.y=x
x=y^2+1
y^2=x-1
y=[square root]x-1; not symmetric

4.(-y)=(-x)^2+1
-y=x^2+1
y=-x^2-1; not symmetric


i understood that pretty well, but what im having trouble with is finding inverses...
example: f(2)=1 g(3)=-2

help!!!

when is the mathmatician project due and how is it suppose to look on the poster

Reflection # 4

Okay, this week went by extremely fast, both in math and in school, partly because we had a 4-day week! I'm glad we got to review domain and range a little bit more this week, and I think I pretty much understand it now. This week, when Mrs. Robinson came back on Thursday, we learned about functions. The main thing I remember about functions are the basic operations of them, including adding, subtracting, multiplying, and dividing them. I will describe these.

f(x) also denotes y, it is like a synonym for y

whenever you see f(x), you plug in x to that f equation

To find (f + g) (x)

It would convert in simpler terms to f(x) + g(x)

Example problem:

f(x) = 2x + 1 g(x) = 2x^2 + 3

Find (f + g) (x)

f(x) + g(x)

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

(f + g) (x) = 2x^2 + 2x + 4

To find (f times g)(x)

It would convert in simpler terms to f(x) times g(x)

Example problem:

f(x) = 4x + 4 g(x) = x - 2x^2

f(x) times g(x)

(4x + 4)(x - 2x^2)

Foil it out.

4x^2 -8x^3 + 4x -8x^2

-8x^3 - 4x^2 + 4x

(f times g) (x) = -8x^3 - 4x^2 + 4x

Also, if it says to find f(g(x)), you plug g(x) into every x in the f equation.

Example:

f(x) = 2x + 1 g(x) = x + 4

f(g(x)) = 2(x + 4) + 1

f(g(x)) = 2x + 8 + 1

f(g(x)) = 2x + 9

Now, I pretty much understand everything. If you think everything through with the functions and inverses, it all makes perfect sense. You just have to apply everything, and plug in your f's and g's of x's correctly.

Reflection #4

okay...this week went by really fast and I really did not understand much that was taught. When Ms. Robinson was not here, we went over domain and range and I grasped that concept a little bit more. I actually understand how to do it. When she came back, we learned functions and how to find inverses. The function part is easy and I know how to do it:

EXAMPLE:

you are given: f(x)= x-2 and g(x)= x+4

Find (f+g)(x)

*you are going to add the two equations together to get the answer.

x-2+x+4
=2x+2
2x=-2

x=-1

_______________________________________________________________

Now, if you are asked to find: f(g(x))

f(x+4)= (x+4) - 2

*always put the "x" in parenthesis incase you have to distribute.

f(x)=x+2

x=-2


_______________________________________________________________

If you are asked to find g(4), then you know your anser is going to come out a number becuase of what is in the parenthesis. So everytime you see an "x" in the equation, you plug in a 4:

g(x)= x^2 - 7

g(4)= 4^2 - 7

= 16 -7

g(x)= 9


_______________________________________________________________

I know we have a quiz on domain and range on monday, and i am glad that i get it, but the only part that i don't get about it is when do you use () or []. I thought you used [] whenever you have a number, but in class, i thought she said something about only use it if you have a fraction, but then on a problem she used [] for a regular number, so if someone can help me out before the quiz, that would be great.

And i also don't get what we did on friday. I know how to draw the reflections and stuff, but i just didn't get how to do the inverses and figure out the horizontal line test.

reflection 4

so this was like a 2 day week, since mrs. robinson wasn't there till thursday. it went by sooooo fast:)..anyway, i didn't get anything that we learned this week. i understood some stuff from section 2, like the (f+g)(x) and the (f-g)(x) and the multiplication ones and the division ones. i think i pretty much understand that. and then the reflection ones, like steps 6-10 in our notes. and then i think i unsertand section 3, when you have....




y=x^2 +1 find any symmetry

1. x-axis
(-y)=x^2+1 NOT SYMMETRIC
y=x^2-1
^^^^reflection X-AXIS






2. y-axis
y=(-x)^2+1 SYMMETRIC
y=x^2+1




3.y=x
x=y^2+1
sqaure root y^2=square root x-1 NO




4.origin
(-y)=(-x)^2+1
-y=x^2+1
y=-x^2-1



something that i don't really understand is the f(f^-1(x))=x stuff. like i get how f^-1 is the inverse but when its all in an equation...i get lost.

Reflection #4

I understand...
How to find if there is any symmetry: y=x^3+4x
1) x-axis: replace y with -y and see if it comes out the same as the original problem
(-y)=x^3+4x------->y=-x^3-4x------->no
2) y-axis: replace x with -x and see if it comes out the same as the original problem
y=(-x)^3+4(-x)------>y=-x^3-4x------->no
3) y=x: swap y and x and solve for y and see if it comes out the same as the original problem
x=y^3+4y------->y(y^2+4)=x------->no
4) origin: replace y with -y and x with -x and see if it comes out the same as the original problem
(-y)=(-x)^3+4(-x)------->-y=-x^3-4x------>y=x^3+4x------->yes

I don't understand...
when you do domain and range, when do you use [ ] and ( )?
I thought it was all numbers get [ ] and all infinities get ( ), but...I don't know!
Will someone please explain?!

reflection 4

Soz, we had another week of school. At least it was a 4 day week. This week was pretty boring, nothing really happened this week. Other than the football game, but we should of won that, and anybody that knows football knows that we shouldve won. Dumb refferees. And im watchin the saints game right now. One questin, when did the lions actually learn how to score? The saints game should count as somethin that happend this week, right? haha well, back to school topics Wow, it was boring when u werent there. and sparky if ur readin this SHUT UP in class XD. and i lost the game, just sayin. I really didnt like last week because we had sooooo much to do, like the periodic table, alot of people gettin sick, and other people that were sick, but not sick enough to stay home, probably thinkin "just let me catch the swine flu already, I feel like doodoo", dont think we can put it in serious terms on here eh? ok, now back to math.......anyways.........math.........o yea, thats the subject with numbers in it right? haha, jk jk, i kno what math is, just havin moments that im spacin out because of the saints game. ok, for real this time, back to math

somethin i did understand was the inverses stuff
its like, f(x)=4x-2 , so u plug it into ur calculator, and c if it only crosses each axis once, and if it does, then it has an inverse
then, u have to switch the x and the y and solve for y, thats how u get f^-1(x)
so u do that for this problem and u get it to come out as f^-1(x)=(x+2)/4, so thats the inverse,
then u check it by plugging the answer and the base problem into f(f^-1(x)) and f^-1(f(x))
if they both come out as x, then u have solved the problem

but one thing i dont understand is the reflections part, it really confuses me

helpppppp.

Alright I have a question about domain and range.

When you do square roots how do you know what the intervals are?

Like if your problems
h(t) = square root of 9-t^2
9-t^2=0
t^2=-9
t=+/-3

I get all of that. Then I know you have to set up the number line. Which was like
f(-4)= square root of 9+4^2= square root of 25
f(0)= square root of 9-0^2= square root of 9
f(4)= square root of 9-4^2= square root of -7

And I know that the only one that didn't work was 4. and -4 and zero worked.
But how do you know what the domain is?

If someone could explain I would appreciate it:)

Oh and If someone could tell me how to figure out what the domain and range is when it gives you a graph.

Thaaaaaaanks!

Reflection 4

This week wasn't that difficult, but we also didn't have that much to do. I would have to say chapter is a little hard. One thing I pretty much understood was finding domain and range.

There are four different ways you can find the domain and range depending on the equation.

The first one is domain & range of all polynomials.
The domain of all polynomials is (-00,00)
The range of all odds: (-00,00)
The range of quadratics: [vertex,00)/positive[-00,vertex]/negative

The second one is the domain and range of fractions.
To find the domain and range of fractions you just set the bottom=0. After doing that solve for y. Then set up your intervals. Which would be (-00,closest number to -00) (<--closest number to -00,closest numberto 00) (closest number to 00,00)

The third one is domain and range of absolute value.
Absolute value for domain is (-00,00)
Range if positive (shift,00)
Range if negative (00,shift)
*Shift is the number that's outside the absolute value.

The fourth one is the domain and range of square roots.
First you would set whats inside the square root equal to 0. Then set up a number line. Try values on either side, (to do this you plug in numbers that you find on the left andthe right of the number on your number line into the equation inside the square root)Eliminate anything negative. Then set upintervals.

Here are some things to remember:
**Notice all domain is (-00,00)
**When talking about vertex in polynomials you use vertex form.
**Domain is x values, Range is y.
**() means included - used for +/-infinity
**[] means not included - used on numbers

----------------------------------------
One thing I really didn't understand was all the f and g stuff
and theres like 10 steps. I don't understand when you have to use which step. I pretty much don't understand any of it but the graphing. If someone wants to explain it too me in an easy way that would really help.

reflection 4

this week was a long and draining week but we learned how to solve for domain, range, find f of x and g of x.
when solving (f+g)(x) you take both equations and and add them up and then solve for x
f(x)=x^2+1 g(x)=x-3
since this is addition, it doesnt matter how you place the numbers together.
but you add like terms together and then you simplify it
x^2+1+x-3
x^2+x-2 and this would be your final answer because it is simplified all the way

when solving (f-g)(x) you subtract both equations in the exact same way that the question is asking you to do.
f(x)= x^2+1 g(x)=x-3
x^2+1-(x-3)
x^2-x+4 and this would be your final answer

im still a little confused on the lesson we did friday