Composite Functions

We started today reviewing Transformations, specifically #'s 13-18 on pg. 80. Be sure that you have a strong understanding of how functions move. 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!
- Remember to meet OUTSIDE tomorrow for class. Meet at the courtyard steps over by the gym!


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; Also complete pg. 80 13-18
- 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

Library of Functions

Today we created a library of 10 functions which you should keep in your notes. Be sure that you have all 10 because it will make transformations much easier if you know what the standard graph looks like. We also talked about reading function values as coordinates and creating the equation of the function using those values. (Section 1.6)

Have a great week!

Coming up:
- Homework: pg. 71 #s 2-24 even, 29, 31, 43, 44
- You will get your tests back Tues. or Wed.

Posting for Points Question:
What is the name of this function: f(x) = c