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even_odd

# even_odd - Even and odd functions A function f is called...

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Even and odd functions A function f is called even provided that = ( ) f - x ( ) f x for all numbers x in the domain of f. If a is a positive number, an even function has the same value at a negative number - a as it has at the corresponding positive number a . An example of an even function is the function f given by = ( ) f x x 2 . The graph of an even function is symmetrical about the y axis . Given a point P ( ) , a ( ) f a on the graph, where a is positive, the point Q ( ) , - a ( ) f a is also on the graph, and the y axis is a right-angle bisector of the line QP, that is, QM = MP and angle QMO is 90 degrees. Examples of even functions . Example 1 : = ( ) f x x 2 . f is even because: = ( ) f - x ( ) - x 2 = ( ) - 1 x 2 = ( ) - 1 2 x 2 = x 2 = ( ) f x . Example 2 : = ( ) f x - x 4 4 x 2 . f is even because: = ( ) f - x - ( ) - x 4 4 ( ) - x 2 = - x 4 4 x 2 = ( ) f x .

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Example 3 : = ( ) f x - 4 x 2 . f is even because: = ( ) f - x - 4 ( ) - x 2 = - 4 x 2 = ( ) f x . Example 4 : = ( ) f x - 4 x . f is even because: = ( ) f - x - 4 - x = - 4 x = ( ) f x . A function f is called odd provided that = ( ) f - x - ( ) f x for all numbers x in the domain of f.
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