Thursday, March 10, 2011
Remember non CAS Calculator
Remember to bring a non-CAS calculator to class tomorrow for our quiz. A TI-83 or 84 is fine or a simple 4-function calculator. I am available before school if you need help with the concepts.
Wednesday, March 9, 2011
8-3 Properties of Inverse Functions
At the start of class we of course reviewed the previous day's homework, which was section 8.2. After our homework review we wet over Mikaela's last post on section 8.2. This took up a good chunk of time. Mr. Cope also talked about how he takes things personally when he doesnt need to. Like when a student falls asleep in his class, it's not his fault. The student definetly should have went to sleep earlier and possibly slept in the previous class so that it didn't happen in Mr. Cope's. We then talked about how Mr. Cope and how he hasn't caught anyone texting during class in a while.
Section 8.3 is about the properties of inverse functions. Here's the basic objective you need to know before you start computing anything:
1. We denote the inverse of a function as f^-1. (f^-1 means the inverse of a function)
2. For every point (a,b) on the graph of f, the point (b,a) is on the inverse graph. (the point (a,b)'s inverse is (b,a))
3. To determine whether the inverse is a function or not without graphing, we apply the horizontal line test. (use the h.l.t. to see if the inverse will be a function without graphing)
Given the general equations y=x, y=x^2, and y=x^3, we know that y=x is a function using h.l.t., y=x^2 is not a function because it doesn't pass h.l.t., and y=x^3 is a function because it passes h.l.t.
The three steps to finding an inverse are...
1. Replacing f(x) with y
2. Switching x and y
3. Solve for y
When combining any two functions the inverse "undo" eachother. For example when we plugged g(f(x)) and f(g(x)) into the calculator both outcomes equaled x.
On a test Mr. Cope may say are these two functions inverses? To solve this you would simply plug the functions into eachother [g(f(x)) and f(g(x))].
The inverse function theorem states that two functions if and only if f(g(x))=x and g(f(x))=x.
The tricky part was power functionsand inverses.
f(x)=x^6's inverse wouldn't be a function because it's a parabola. Parabolas never ever pass h.l.t. It causes a problem when you attempt to plug negative numbers into the inverse function. X can't be negative in an inverse. So to take care of that you can restrict the domain to X is greater than or equal to 0.
f(x)=x^an odd number passes h.l.t., and is much simpler than an even power function.
Next blogger is... Emma B!
Section 8.3 is about the properties of inverse functions. Here's the basic objective you need to know before you start computing anything:
1. We denote the inverse of a function as f^-1. (f^-1 means the inverse of a function)
2. For every point (a,b) on the graph of f, the point (b,a) is on the inverse graph. (the point (a,b)'s inverse is (b,a))
3. To determine whether the inverse is a function or not without graphing, we apply the horizontal line test. (use the h.l.t. to see if the inverse will be a function without graphing)
Given the general equations y=x, y=x^2, and y=x^3, we know that y=x is a function using h.l.t., y=x^2 is not a function because it doesn't pass h.l.t., and y=x^3 is a function because it passes h.l.t.
The three steps to finding an inverse are...
1. Replacing f(x) with y
2. Switching x and y
3. Solve for y
When combining any two functions the inverse "undo" eachother. For example when we plugged g(f(x)) and f(g(x)) into the calculator both outcomes equaled x.
On a test Mr. Cope may say are these two functions inverses? To solve this you would simply plug the functions into eachother [g(f(x)) and f(g(x))].
The inverse function theorem states that two functions if and only if f(g(x))=x and g(f(x))=x.
The tricky part was power functionsand inverses.
f(x)=x^6's inverse wouldn't be a function because it's a parabola. Parabolas never ever pass h.l.t. It causes a problem when you attempt to plug negative numbers into the inverse function. X can't be negative in an inverse. So to take care of that you can restrict the domain to X is greater than or equal to 0.
f(x)=x^an odd number passes h.l.t., and is much simpler than an even power function.
Next blogger is... Emma B!
Tuesday, March 8, 2011
A couple days ago we took the chapter 7 test. This test consisted of two parts: a no calc. section but we were able to use our "green cards" and then a calculator section.
In preparation for this test we had a review sheet the day before. This review sheet first discussed what would be on the no calc. part: it went over power functions, geometric sequences with recursive,explicit formula and domain and range. Also on the review sheet Mr. Cope gave us practice problems that required us to use properties of powers with negative and fractional exponents. On the back of the sheet it discussed the calculator part of the test: topics it covered were compound interest,word problems, and using properties of powers with numbers not on the "green card".
If you had trouble with any of these topics or problems remember you can always refer to moodle or your notes from class.
Something I recommend when we are reviewing before the test that you(Mr.cope) actually discuss and go over it with us in class rather than us just doing it ourselves and making us go on moodle if we want to check our answers because im a sure most of us forget and just wing it on the test not even knowing if we did the problems correctly.
And as far as the test goes I don't think there should be a no calc. part because the majority of the quiz's you gave us for this chapter were no calc. and us as students tend to not do as well on them, therefore bringing down our scores. but overall the test was ok, I just wish I had more review and better assistance from the teacher.
mikaela allmon
In preparation for this test we had a review sheet the day before. This review sheet first discussed what would be on the no calc. part: it went over power functions, geometric sequences with recursive,explicit formula and domain and range. Also on the review sheet Mr. Cope gave us practice problems that required us to use properties of powers with negative and fractional exponents. On the back of the sheet it discussed the calculator part of the test: topics it covered were compound interest,word problems, and using properties of powers with numbers not on the "green card".
If you had trouble with any of these topics or problems remember you can always refer to moodle or your notes from class.
Something I recommend when we are reviewing before the test that you(Mr.cope) actually discuss and go over it with us in class rather than us just doing it ourselves and making us go on moodle if we want to check our answers because im a sure most of us forget and just wing it on the test not even knowing if we did the problems correctly.
And as far as the test goes I don't think there should be a no calc. part because the majority of the quiz's you gave us for this chapter were no calc. and us as students tend to not do as well on them, therefore bringing down our scores. but overall the test was ok, I just wish I had more review and better assistance from the teacher.
mikaela allmon
Tuesday, March 8th, 2011 Lesson 8.2
Today in class we went over the homework we had over the weekend which was 801, then viewed the blog. Mr. Cope gave us the rubric on how we would be graded for the blog posts, then started the lesson.
Lesson 8.2: Inverses of Relations
3 Important things to know about inverses of relations:
Suppose f is a relation and g is the inverse of f;
1) A rule (or equation) can be found by switching x and y (solving for y if necessary)
2) A graph for g is found by reflecting f over y=x,
3) The domain of g is the range of f, and the range of g is the domain of f
An example of inverse relation is this;
Let f = (1,4) (2,8) (3,8) (0,0) (-1,-4)
The inverse relation of this would be;
(4,1) (8,2) (8,3) (0,0) (-4,-1)
Another thing to note, is that the f is a function but the inverse of f is not.
This is because when you reverse x and y, there becomes (8,2) and (8,3) which means it is not a function.
You can also find out if the inverse is a function by seeing if it passes the horizontal line test.
The domain of f is ( 1, 2, 3, 0, -1) and the range is ( 4, 8, 0, -4)
The domain of the inverse is (4, 8, 0, -4) and the range is (1, 2, 3, 0, -1)
You should note that the domain and range swap when it is the inverse.
Another example is f 9x0 = 1/2x + 4
The work I did to find the inverse is;
I rewrote the equation to be y = 1/2x + 4
Then rewrote it as x = 1/2y + 4
Then I subtracted the 4
So its now x - 4 = 1/2y
Then I multiplied both sides by 2 to get ride of the fraction
So it would now be 2x-8 = y which is the final answer.
I hope this helps!
Homework :
802 and the 3 problems on the back of the worksheet.
The next scribe will be Leah.
Wednesday, March 2, 2011
March 03, 2011
It has been yet another wonderful day in Mr.Cope's second period Advanced Algebra class.
First we started our day off by getting a homework quiz, which usually either helps your grade or hurts it. Along with going over our partner quizzes, that were not so phenomenal according to Mr.Cope and the would not count for points, so hurray for those who did not so great. We then received our very structured and helpful Chapter 7 review sheet that we did in class, and Mr.Cope so kindly reminded us that we should access Moodle, that has many helpful resources, such as extra copies of our green cards that we are allowed to use for tomorrow's Chapter 7 test, and there are also review sheets and answers on Moodle for those that are interested.
Don't forget to study for our Chapter 7 test tomorrow, :)
Good luck.
btw, Mikaela your next.
First we started our day off by getting a homework quiz, which usually either helps your grade or hurts it. Along with going over our partner quizzes, that were not so phenomenal according to Mr.Cope and the would not count for points, so hurray for those who did not so great. We then received our very structured and helpful Chapter 7 review sheet that we did in class, and Mr.Cope so kindly reminded us that we should access Moodle, that has many helpful resources, such as extra copies of our green cards that we are allowed to use for tomorrow's Chapter 7 test, and there are also review sheets and answers on Moodle for those that are interested.
Don't forget to study for our Chapter 7 test tomorrow, :)
Good luck.
btw, Mikaela your next.
Tuesday, March 1, 2011
3/1/2011
Hey everyone! Today in class we went over the homework (708 A & B) and then we took a partner, open-note, no calc quiz! Also, we talked more about this blog and what we think of it. There were varying opinions on it, ranging from 'I don't think this is going to have any affect on anyone' to 'I really like that we will get to interact and almost talk to each other!'
Okay, so Victoria G is going to post the next one! :)
Reflections from Class
I just wanted to say thank you for your honest reflections today in class about what this blogging process will be like. I do want it to succeed, but I don't have any delusions that it will be amazing and revolutionary right away. If it turns into something great, it will take time and effort on both of our parts. We will need to reflect on and share what is working well and what needs to be improved. I appreciate your patience and your willingness to give it a try.
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