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Even and odd functions.
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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
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