Mathematical Modeling

We spent the first part of class finishing up the "expert group" presentations and answering any questions about the test material. Be sure that you correct and review all of these problems for your test Wednesday.

After the "expert groups" we introduced Mathematical Modeling, the process of analyzing and interpreting data. We learned the process for graphing statistical data, as well as finding the Linear Regression line for any set of points. Remember, when looking at a linear regression line you use the correlation coefficient to determine how exact your line fits the given data. The closer to 1, the better the fit. If you need a review of how to graph this data on the calculator click the link to the right.

For this weekend you need to do some research on the exponential growth of the Starbucks franchise. You should use the link on the right and navigate through until you find the Company Timeline. Read over the timeline as it gives interesting information. As you go through the information create a table of growth since the first franchise. Your first year will be 1971 when the first Starbucks opened in Seattle. Start this year as 0, and continue up from there. Notice that there will not be a number for every year, so only include what is given in this timeline. We will use this data next week!

Coming up:
- Homework: Create a table of values for the year and # of Starbucks stores at the end of that given year.
- Test will be Wednesday October 10th!

Posting for Points:
Where was the first Starbucks? Are you a Starbucks fan?

Test Review

Today we reviewed the material that will be on your test this coming Wednesday. Please remember that this test will be cumulative!

Tomorrow we will begin looking at new material that will not be expected for the test.

Coming up:

- Test on Wednesday October 10th

- "Midterm" coming up on October 17th

Posting for Points:

What does it mean if you find the fog and gof of two functions to both equal "x"?

Inverse Functions

Today we went over your assignment from page 99, dealing with inverse functions. We got through most of the assignment but will begin tomorrow by completing problem #24. You should rework this problem before class. Remember that there are two methods for solving these problems, and in situations like #23 and #24 you should use the gof and fog methods as discussed in class. If you were not in class please refer to the book for examples (pg. 93-99).
I have decided that the test will be moved to WEDNESDAY, October 10th. Please begin studying now because we will move on to new material starting Monday!

Coming up:
- TEST: Wed. October 10th (remember that the test is cumulative)
- No Homework, but begin studying!

Posting for Points:
What is the BEST method for determining if one given equation is the inverse of another inverse equation?

Stuck in the Airport

I am stuck in the airport until late tonight but just wanted to remind you that you should have both Monday and Tuesday's assignments done by tomorrow. If you have not done them already, be sure to finish them tonight!

See you tomorrow!

Coming up:

- Both assignments due tomorrow (from Monday and Tuesday)

Posting for Points:

Who has the worst luck with flying?

Composite Functions

We started today reviewing Transformations, specifically # 6 on pg. 79. Be sure that you have a strong understanding of how functions move. If you were not in class get the notes/examples dealing with stretch and shrink. Remember to check out the link on the right if you are still having trouble with transformations.
We took a few notes on Composite Functions (basically operations for putting two functions together). Be sure that you simplify all of your composite functions!

Coming up:
- Homework: pg. 89 #'s 6-12 even, 17, 18, 31, 33
- Your next test is October 5th!

Posting for Points:
When is your next test?

Translations

We went over translations during the entire class period today! Hopefully you are beginning to see how these functions move, but it can take some time before this material really clicks. Be sure to check out the websites on the right, especially "Visual Functions," if you are still having trouble with these problems. We will spend a few minutes tomorrow going over Transformations, but then we will be moving on to Composite Functions.

Composite functions are pretty easy because it is just performing basic operations on 2 functions instead of 1.
For example, (f+g)(x) = f(x) + g(x)....so if f(x) = x + 3 and g(x) = 2x + 2 then,
(f+g)(x) = (x +3) + (2x + 2).....or simplified.... (f+g)(x) = 3x + 5

We will go over this tomorrow but you should look through the examples on pages 84-85 before class. This is your only homework, other than the question below, but make sure you do it!

Have a great day!

Coming up:
- Homework: Read over pages 84-85 and review your homework from last night
- Your next test will be Friday, October 5th!

Posting for Points:
Using your book and/or the brief notes from above, what would (f - g)(x) equal ? (it follows the same pattern as above)

Transformations

A few key points from last night's homework:
a) be sure that you have corrected the Greatest Integer Function as always rounding DOWN!
b) review how to read function values as coordinates.
After reviewing the homework we created a key for Transformations (the way our standard graphs move). You should keep these notes with your Library of Functions.
For tonight be sure that you check out the website under math links labeled "Visual Functions." This website should help you visualize how translations occur. (Section 1.7)

Have a great day!

Coming up:
- Homework: pg. 79 #'s 1, 2, 4, 5, 9-12
- You will get your tests back tomorrow!

Posting for Points Question:
How will this function move from our standard graph of f(x)=x:
f(x)= x + 3