Successfully reported this slideshow.
Upcoming SlideShare
×

Pre-Cal 40S Slides March 3, 2008

683 views

Published on

Inverse functions: 4 perspectives.

Published in: Technology, Education
• Full Name
Comment goes here.

Are you sure you want to Yes No
• Be the first to comment

• Be the first to like this

Pre-Cal 40S Slides March 3, 2008

1. 1. Baby Play or All About Inverse Functions duck wrangling by toyfoto
2. 2. 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
3. 3. 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) 1. ƒ(x) = x³ - x 2. g(x) = x³- x² Examples: 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
4. 4. Are these functions even or odd? Justify your answers algebraically. g(x) = x3+ 3x ƒ(x) = x4+ 2x2+ 3
5. 5. ƒ is an odd function. COMPLETE THE GRAPH.
6. 6. Baby Play or All About Inverse Functions duck wrangling by toyfoto
7. 7. Inverses ... The concept ... Numerically speaking ...
8. 8. Inverses ... Algebraically speaking ... Conceptually analyzing the function ...
9. 9. Inverses ... Graphically speaking ...