AP Calculus Slides September 18, 2007
Upcoming SlideShare
Loading in...5
×
 

Like this? Share it with your network

Share

AP Calculus Slides September 18, 2007

on

  • 1,753 views

Operations on functions, characteristics of polynomial and rational functions, even and odd functions.

Operations on functions, characteristics of polynomial and rational functions, even and odd functions.

Statistics

Views

Total Views
1,753
Views on SlideShare
1,744
Embed Views
9

Actions

Likes
0
Downloads
13
Comments
0

2 Embeds 9

http://apcalc07.blogspot.com 8
http://www.slideshare.net 1

Accessibility

Categories

Upload Details

Uploaded via as Adobe PDF

Usage Rights

© All Rights Reserved

Report content

Flagged as inappropriate Flag as inappropriate
Flag as inappropriate

Select your reason for flagging this presentation as inappropriate.

Cancel
  • Full Name Full Name Comment goes here.
    Are you sure you want to
    Your message goes here
    Processing…
Post Comment
Edit your comment

AP Calculus Slides September 18, 2007 Presentation Transcript

  • 1. Operations on Functions Surgeons
  • 2. and their domains. For each of the following find Domain: Domain: Domain: Domain:
  • 3. and their domains. For each of the following find Domain: Domain: Domain: Domain:
  • 4. and their domains. For each of the following find Domain: Domain: Domain: Domain:
  • 5. Using your calculator, find the coordinates of the the quot;turning pointquot; of ƒ in quadrant II.
  • 6. Graph the rational function ƒ. State the domain and range and determine left- and right-hand asymptotes numerically.
  • 7. Graph the rational function ƒ. State the domain and range and determine left- and right-hand asymptotes numerically.
  • 8. a little review ...
  • 9. EVEN FUNCTIONS Graphically: A function is quot;evenquot; if its graph is symmetrical about the y-axis. These functions are even... These are not ... Symbolically (Algebraically) a function is quot;evenquot; IFF (if and only if) ƒ(-x) = ƒ(x) Examples: Are these functions even? 1. f(x) = x² 2. g(x) = x² + 2x f(-x) = (-x)² g(-x) = (-x)² + 2(-x) f(-x) = x² g(-x) = x² - 2x since f(-x)=f(x) since g(-x) is not equal to g(x) f is an even function g is not an even function
  • 10. ODD FUNCTIONS Graphically: A function is quot;oddquot; if its graph is symmetrical about the origin. These functions These are are odd ... not ... Symbolically (Algebraically) a function is quot;oddquot; IFF (if and only if) ƒ(-x) = -ƒ(x) Examples: 1. ƒ(x) = x³ - x 2. g(x) = x³- x² ƒ(-x) = (-x)³ - (-x) g(-x) = (-x)³ - (-x)² ƒ(x) = -x³ + x g(x) = -x³ - x² -ƒ(x) = -(x³ - x) -g(x) = -(x³-x²) -ƒ(x) = -x³ + x -g(x) = -x³+ x² since ƒ(-x)= -ƒ(x) since g(-x) is not equal to -g(x) ƒ is an odd function g is not an odd function
  • 11. Demonstrate, in as many different ways as you can think of, whether the function ƒ is even, odd or neither.