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f(-x) = f(x)  Even Function

Proving and Demonstrating that Functions are Even and Odd. f(-x) = f(x)  Even Function. f(-x) = -f(x)  Odd Function. f(x). f(-x). f(x). -x. x. x. -x. f(-x). f(-x) is the opposite of f(x). f(-x) is the same as f(x). so, f(-x)= - f(x). so, f(-x)= f(x).

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f(-x) = f(x)  Even Function

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  1. Proving and Demonstrating that Functions are Even and Odd f(-x) = f(x)  Even Function f(-x) = -f(x)  Odd Function f(x) f(-x) f(x) -x x x -x f(-x) f(-x) is the opposite of f(x) f(-x) is the same as f(x) so, f(-x)= - f(x) so, f(-x)= f(x)

  2. Proving and Demonstrating that Functions are Even and Odd f(-x) = f(x)  Even Function Example: is y = x2 even? odd? f(-x) = (-x)2 =x2 f(x) = x2 -f(x) = -(x)2 = -x2 -f(x) = f(-x)  Odd Function Example: is y = x3 even? odd? f(-x) = (-x)3 =-x3 f(x) = x3 -f(x) = -(x)3 =-x3 Prove Same  Even Same Odd Demonstrate Maps onto itself after a rotation of 1800 Odd Maps onto itself after a reflection over the y-axis  Even

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