Main Concept

A function $f$ is even if for any $x$ in the domain of $f$ we have $f\left(-x\right)\=f\left(x\right)$. Note that this means the domain of $f$ must be symmetric about 0, since $-x$ must be in the domain whenever $x$ is. An  even function is symmetric with respect to the vertical (y) axis.

A function $f$ is odd if for any $x$ in the domain of $f$ we have $f\left(-x\right)\= -f\left(x\right)$. Note that this means that the domain of $f$ must be symmetric about 0, since $-x$ must be in the domain whenever $x$ is. An odd function is symmetric with respect to the origin.

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MathApps/FunctionsAndRelations