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Unformatted text preview: 2 4 2 4 ) ( x x x f-= A function f is odd if, for all x in the domain of f , ). ( ) ( x f x f-=-In other words, functions whose graphs are symmetric with respect to the origin are odd functions . Example: x x x f 3 ) ( 3-= A function f is neither even nor odd if it does not satisfy the conditions for either. Example: x x x f 2 ) ( 2 + = Symmetry Additional Examples Ex 1. Draw something that shows each of these symmetries. Symmetry with respect Symmetry with respect Symmetry with respect to the x-axis to the y-axis to the origin Ex 2. Find the point that is symmetric to (-3,2) with respect to the x-axis, y-axis, and origin. Ex 3. Test algebraically whether 2 4 3 2 y x = + is symmetric with respect to the x-axis, y-axis, and origin. Even and Odd Functions Ex 4. Determine if the following functions are even, odd, or neither. A. 4 ) ( 2 +-= x x f B. x x x x f 2 6 5 ) ( 3 7--= C. 7 3 5 ) ( 2 6--= x x x h...
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