OK, Really this time, Even and uh ... ODD (?)

Functions~ BLINK ~ by flickr user ViaMoi

Given A(-2, -3) find the coordinates of its image under the transformation given above.

The image of point B after the transformation shown above is (1, 4). Find the original coordinates of B.

EVEN FUNCTIONSGraphically: A function is "even" if its graph is symmetrical about the y-axis.

These are not ...

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 - 2xsince f(-x)=f(x) since g(-x) is not equal to g(x)f is an even function g is not an even function

Symbolically (Algebraically)a function is "even" IFF (if and only if) ƒ(-x) = ƒ(x)

These functions are even...

ODD FUNCTIONSGraphically: A function is "odd" if its graph is symmetrical about the origin.

These are not ...

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

These functions are odd ...

Symbolically (Algebraically)a function is "odd" IFF (if and only if) ƒ(-x) = -ƒ(x)

Examples:

Are these functions even or odd? Justify your answers algebraically.

g(x) = x + 3x3ƒ(x) = x + 2x + 324