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How do you determine if a function is odd or even degree

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sometimes you can just look at the equation itself \[y = x^5 + 2x^3 + x\] all the exponents of x in this equation are 1,3 and 5..all are odd..therefore this is an odd function \[y = 2x^2 + 4\] the exponents are 2 and 0..both are even therefore this is an even function note that this can only be applied sometimes

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Other answers:

the simple test is to substitute -x for x if f(-x) = f(x) the function is even ... e,g, f(x) = x^2 f(-x) = (-x)^2 = x^2 id f(-x) = -f(x) the function is odd e.g f(x) = x^3 f(-x) = (-x)^3 = -x^3 the function can also be neither odd nor even as an example f(-x) = x^3 + 1 = -x^3 + 1 which isn't the negative of the original function.

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