Tuesday, March 22, 2011
Scroll to the bottom and you can create the symbol you need. Then copy and paste into your document or blog post. Let me know if you encounter problems.
Monday, March 21, 2011
= Undefined (no matter what your calculator says, and it will say many things….)
Have Fun doing the homework. I know I will.
Have Fun doing the homework. I know I will.
Thursday, March 17, 2011
Tuesday, March 15, 2011
Monday, March 14, 2011
Today we got the results back from our 8.1-8.3 quiz. Overall, the class did pretty well; the average was and 80%. We went over a few problems but there was little confusion so we moved on.
Next, since we didn't have any homework, we skipped right to the lesson, 8.4. To begin lesson 8.4, Radical Notation for nth Roots, we reviewed some of the ideas from previous sections that are critical in understanding this one. The two most important are probably: an
x1/2 = √x
n√xm = xm/n
A useful example (from the notes) is:
Suppose x ≥ 0. Simplify 3√x12.
What you should do is take (x12) and raise it to the 1/3 power.
(x12)1/3 = x4
In lesson 8.4, however, it gets a little more complex. I hope I can help you understand it. Instead of being formatted like the example above, problems in this section look a little more like this:
Suppose x ≥ 0. Rewrite √(√(√x))). It’s pretty tough to write that on word, but it’s basically the square root, of the square root, of the square root of x. You would write it using radical exponents, like so:
((x½) ½) ½ or, since you multiply ½ by ½ by ½, its x1/8.
So, if you suppose x ≥ 0, can you solve 6√y4 ?
Here is how you would: (y4)1/6 = y4/6 = y2/3
The homework for tomorrow is As. 804. I hope this was helpful! If you have any questions, the notes are on moodle: http://gbs-moodle.glenbrook225.org/moodle/login/index.php
Sunday, March 13, 2011
Thursday, March 10, 2011
Here are some resources:
-You can look on Moodle for
1. Chapter 8 homework answers
2. Chapter 8 notes
3. 8.1-8.3 review key
4. You are also able to access the online textbook
-In the textbook
1.Page 516- Page 536 is lesson 8.1-8.3
2.Page 574- Page 577 is the review section.
Sorry...This is not one of my best sections. I'm still reviewing. Next post will be better!!
Wednesday, March 9, 2011
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
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.
Wednesday, March 2, 2011
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, :)
btw, Mikaela your next.