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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 xaxis to the yaxis to the origin Ex 2. Find the point that is symmetric to (3,2) with respect to the xaxis, yaxis, and origin. Ex 3. Test algebraically whether 2 4 3 2 y x = + is symmetric with respect to the xaxis, yaxis, 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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This note was uploaded on 08/14/2008 for the course MATH 1111 taught by Professor Teachey during the Summer '08 term at Kennesaw.
 Summer '08
 Teachey
 Math, Algebra

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