7/25/2019 Even and Odd Function

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A function is odd if f(x) = -f(-x) for all values of x.A function is even if f(x) = f(-x) for all values of x.

f(x) = sin x, f(x) = tan x, f(x) = csc x, f(x) = cot x are all odd.f(x) = cos x, f(x) = sec x are both even.

You might like to remember a few more facts about these sorts of functions.The sum of odd functions is odd.The sum of even functions is even.The sum of odd and even functions is neither.The product of functions works similarly to the facts about positive and negative numbers, i.e. product of odd functions is odd.

Another way to look at it is by symmetry.An even function has reflective symmetry about the y axis.An odd function has rotational symmetry around the origin.